# Specified Positive-Scale Triangle Similarity Foundations

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This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261006-advance-20261007-r06-similarity-foundations · 2026-10-06 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(6, -4), B3=(4, -6), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=1/1. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[9, 5, 8] and B=[9, 5, 8]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0001/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 2. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(9, -4), B3=(5, -8), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=3/1. Does this scale fit every corresponding side?

View answer and explanationNo

The squared sides are A=[9, 5, 8] and B=[36, 20, 32]. Check B²q²=A²p² on each corresponding side, obtaining No. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0002/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 3. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(12, -4), B3=(6, -10), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=3/1. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[9, 5, 8] and B=[81, 45, 72]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0003/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 4. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(6, 0), A3=(2, 4) and B1=(3, -4), B2=(24, -4), B3=(10, -18), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=7/2. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[36, 20, 32] and B=[441, 245, 392]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0004/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 5. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(18, -4), B3=(8, -14), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=5/1. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[9, 5, 8] and B=[225, 125, 200]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0005/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 6. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(21, -4), B3=(9, -16), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=7/1. Does this scale fit every corresponding side?

View answer and explanationNo

The squared sides are A=[9, 5, 8] and B=[324, 180, 288]. Check B²q²=A²p² on each corresponding side, obtaining No. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0006/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 7. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(24, -4), B3=(11, -18), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=7/1. Does this scale fit every corresponding side?

View answer and explanationNo

The squared sides are A=[9, 5, 8] and B=[441, 260, 365]. Check B²q²=A²p² on each corresponding side, obtaining No. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0007/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 8. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(27, -4), B3=(11, -20), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=9/1. Does this scale fit every corresponding side?

View answer and explanationNo

The squared sides are A=[9, 5, 8] and B=[576, 320, 512]. Check B²q²=A²p² on each corresponding side, obtaining No. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0008/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 9. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(6, 0), A3=(2, 4) and B1=(3, -4), B2=(54, -4), B3=(20, -38), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=17/2. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[36, 20, 32] and B=[2601, 1445, 2312]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0009/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 10. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(33, -4), B3=(13, -24), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=11/1. Does this scale fit every corresponding side?

View answer and explanationNo

The squared sides are A=[9, 5, 8] and B=[900, 500, 800]. Check B²q²=A²p² on each corresponding side, obtaining No. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0010/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 11. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(36, -4), B3=(14, -26), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=11/1. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[9, 5, 8] and B=[1089, 605, 968]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0011/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 12. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(39, -4), B3=(15, -28), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=13/1. Does this scale fit every corresponding side?

View answer and explanationNo

The squared sides are A=[9, 5, 8] and B=[1296, 720, 1152]. Check B²q²=A²p² on each corresponding side, obtaining No. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0012/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 13. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(42, -4), B3=(16, -30), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=13/1. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[9, 5, 8] and B=[1521, 845, 1352]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0013/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 14. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(6, 0), A3=(2, 4) and B1=(3, -4), B2=(84, -4), B3=(31, -58), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=27/2. Does this scale fit every corresponding side?

View answer and explanationNo

The squared sides are A=[36, 20, 32] and B=[6561, 3700, 5725]. Check B²q²=A²p² on each corresponding side, obtaining No. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0014/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 15. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(48, -4), B3=(18, -34), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=15/1. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[9, 5, 8] and B=[2025, 1125, 1800]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0015/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 16. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(51, -4), B3=(19, -36), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=17/1. Does this scale fit every corresponding side?

View answer and explanationNo

The squared sides are A=[9, 5, 8] and B=[2304, 1280, 2048]. Check B²q²=A²p² on each corresponding side, obtaining No. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0016/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 17. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(54, -4), B3=(20, -38), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=17/1. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[9, 5, 8] and B=[2601, 1445, 2312]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0017/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 18. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(57, -4), B3=(21, -40), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=19/1. Does this scale fit every corresponding side?

View answer and explanationNo

The squared sides are A=[9, 5, 8] and B=[2916, 1620, 2592]. Check B²q²=A²p² on each corresponding side, obtaining No. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0018/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 19. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(6, 0), A3=(2, 4) and B1=(3, -4), B2=(114, -4), B3=(40, -78), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=37/2. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[36, 20, 32] and B=[12321, 6845, 10952]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0019/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 20. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(63, -4), B3=(23, -44), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=21/1. Does this scale fit every corresponding side?

View answer and explanationNo

The squared sides are A=[9, 5, 8] and B=[3600, 2000, 3200]. Check B²q²=A²p² on each corresponding side, obtaining No. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0020/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 21. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(66, -4), B3=(25, -46), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=21/1. Does this scale fit every corresponding side?

View answer and explanationNo

The squared sides are A=[9, 5, 8] and B=[3969, 2248, 3445]. Check B²q²=A²p² on each corresponding side, obtaining No. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0021/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 22. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(69, -4), B3=(25, -48), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=23/1. Does this scale fit every corresponding side?

View answer and explanationNo

The squared sides are A=[9, 5, 8] and B=[4356, 2420, 3872]. Check B²q²=A²p² on each corresponding side, obtaining No. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0022/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 23. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(72, -4), B3=(26, -50), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=23/1. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[9, 5, 8] and B=[4761, 2645, 4232]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0023/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 24. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(6, 0), A3=(2, 4) and B1=(3, -4), B2=(144, -4), B3=(50, -98), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=47/2. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[36, 20, 32] and B=[19881, 11045, 17672]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0024/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 25. Labeled Similarity at a Specified Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. The ordered nondegenerate triangles have A1=(0, 0), A2=(3, 0), A3=(1, 2) and B1=(3, -4), B2=(78, -4), B3=(28, -54), with explicit correspondence A1↔B1, A2↔B2, A3↔B3. The specified positive length scale from A to B is k=25/1. Does this scale fit every corresponding side?

View answer and explanationYes

The squared sides are A=[9, 5, 8] and B=[5625, 3125, 5000]. Check B²q²=A²p² on each corresponding side, obtaining Yes. Rejecting this specified scale witness does not reject another possible scale or change the vertex correspondence.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0025/)

Labeled triangle similarity with a specified positive scale · qf-similarity-specified-scale · candidate





## 26. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=-12/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0026/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 27. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=-11/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0027/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 28. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=-10/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0028/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 29. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=-9/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0029/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 30. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=-8/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0030/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 31. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=-7/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0031/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 32. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=-6/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0032/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 33. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=-5/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0033/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 34. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=-4/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0034/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 35. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=-3/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0035/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 36. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=-2/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0036/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 37. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=-1/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0037/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 38. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=0/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationNo

The denominator is valid, and the numerator must also be positive, giving No. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0038/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 39. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=1/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationYes

The denominator is valid, and the numerator must also be positive, giving Yes. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0039/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 40. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=2/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationYes

The denominator is valid, and the numerator must also be positive, giving Yes. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0040/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 41. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=3/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationYes

The denominator is valid, and the numerator must also be positive, giving Yes. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0041/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 42. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=4/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationYes

The denominator is valid, and the numerator must also be positive, giving Yes. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0042/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 43. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=5/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationYes

The denominator is valid, and the numerator must also be positive, giving Yes. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0043/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 44. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=6/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationYes

The denominator is valid, and the numerator must also be positive, giving Yes. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0044/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 45. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=7/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationYes

The denominator is valid, and the numerator must also be positive, giving Yes. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0045/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 46. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=8/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationYes

The denominator is valid, and the numerator must also be positive, giving Yes. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0046/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 47. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=9/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationYes

The denominator is valid, and the numerator must also be positive, giving Yes. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0047/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 48. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=10/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationYes

The denominator is valid, and the numerator must also be positive, giving Yes. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0048/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 49. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=11/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationYes

The denominator is valid, and the numerator must also be positive, giving Yes. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0049/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 50. Positive Length-Scale Eligibility

Use one equal-unit orthonormal Euclidean Cartesian frame. With positive denominator q=1, is k=12/1 an eligible positive length scale for nondegenerate similarity?

View answer and explanationYes

The denominator is valid, and the numerator must also be positive, giving Yes. Zero or negative candidates fail this positive-length-scale convention; do not reinterpret them as signed coordinate coefficients.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0050/)

Labeled triangle similarity with a specified positive scale · qf-similarity-positive-ratio · candidate





## 51. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 2>0. At corresponding positive length scale k=1/1, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation2/1

Multiply the given positive squared length by k² to obtain 2/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0051/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 52. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 5>0. At corresponding positive length scale k=2/2, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation5/1

Multiply the given positive squared length by k² to obtain 5/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0052/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 53. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 10>0. At corresponding positive length scale k=3/3, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation10/1

Multiply the given positive squared length by k² to obtain 10/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0053/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 54. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 17>0. At corresponding positive length scale k=4/1, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation272/1

Multiply the given positive squared length by k² to obtain 272/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0054/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 55. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 26>0. At corresponding positive length scale k=5/2, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation325/2

Multiply the given positive squared length by k² to obtain 325/2. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0055/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 56. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 37>0. At corresponding positive length scale k=1/3, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation37/9

Multiply the given positive squared length by k² to obtain 37/9. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0056/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 57. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 50>0. At corresponding positive length scale k=2/1, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation200/1

Multiply the given positive squared length by k² to obtain 200/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0057/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 58. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 65>0. At corresponding positive length scale k=3/2, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation585/4

Multiply the given positive squared length by k² to obtain 585/4. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0058/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 59. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 82>0. At corresponding positive length scale k=4/3, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation1312/9

Multiply the given positive squared length by k² to obtain 1312/9. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0059/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 60. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 101>0. At corresponding positive length scale k=5/1, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation2525/1

Multiply the given positive squared length by k² to obtain 2525/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0060/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 61. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 122>0. At corresponding positive length scale k=1/2, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation61/2

Multiply the given positive squared length by k² to obtain 61/2. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0061/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 62. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 145>0. At corresponding positive length scale k=2/3, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation580/9

Multiply the given positive squared length by k² to obtain 580/9. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0062/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 63. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 170>0. At corresponding positive length scale k=3/1, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation1530/1

Multiply the given positive squared length by k² to obtain 1530/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0063/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 64. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 197>0. At corresponding positive length scale k=4/2, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation788/1

Multiply the given positive squared length by k² to obtain 788/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0064/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 65. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 226>0. At corresponding positive length scale k=5/3, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation5650/9

Multiply the given positive squared length by k² to obtain 5650/9. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0065/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 66. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 257>0. At corresponding positive length scale k=1/1, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation257/1

Multiply the given positive squared length by k² to obtain 257/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0066/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 67. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 290>0. At corresponding positive length scale k=2/2, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation290/1

Multiply the given positive squared length by k² to obtain 290/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0067/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 68. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 325>0. At corresponding positive length scale k=3/3, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation325/1

Multiply the given positive squared length by k² to obtain 325/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0068/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 69. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 362>0. At corresponding positive length scale k=4/1, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation5792/1

Multiply the given positive squared length by k² to obtain 5792/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0069/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 70. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 401>0. At corresponding positive length scale k=5/2, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation10025/4

Multiply the given positive squared length by k² to obtain 10025/4. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0070/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 71. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 442>0. At corresponding positive length scale k=1/3, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation442/9

Multiply the given positive squared length by k² to obtain 442/9. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0071/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 72. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 485>0. At corresponding positive length scale k=2/1, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation1940/1

Multiply the given positive squared length by k² to obtain 1940/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0072/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 73. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 530>0. At corresponding positive length scale k=3/2, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation2385/2

Multiply the given positive squared length by k² to obtain 2385/2. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0073/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 74. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 577>0. At corresponding positive length scale k=4/3, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation9232/9

Multiply the given positive squared length by k² to obtain 9232/9. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0074/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 75. Squared Side Length under a Positive Scale

Use one equal-unit orthonormal Euclidean Cartesian frame. A side of a nondegenerate triangle has given squared length 626>0. At corresponding positive length scale k=5/1, find its scaled squared length. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation15650/1

Multiply the given positive squared length by k² to obtain 15650/1. Length scales by k, but squared length scales by k²; this is exact conversion of the supplied quantity.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0075/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-squared-side · candidate





## 76. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 1/2>0 squared units. At corresponding positive length scale k=1/1, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation1/2

Multiply the given positive area by k² to obtain 1/2 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0076/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 77. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 3/2>0 squared units. At corresponding positive length scale k=2/2, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation3/2

Multiply the given positive area by k² to obtain 3/2 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0077/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 78. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 5/2>0 squared units. At corresponding positive length scale k=3/3, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation5/2

Multiply the given positive area by k² to obtain 5/2 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0078/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 79. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 7/2>0 squared units. At corresponding positive length scale k=4/1, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation56/1

Multiply the given positive area by k² to obtain 56/1 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0079/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 80. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 9/2>0 squared units. At corresponding positive length scale k=1/2, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation9/8

Multiply the given positive area by k² to obtain 9/8 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0080/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 81. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 11/2>0 squared units. At corresponding positive length scale k=2/3, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation22/9

Multiply the given positive area by k² to obtain 22/9 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0081/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 82. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 13/2>0 squared units. At corresponding positive length scale k=3/1, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation117/2

Multiply the given positive area by k² to obtain 117/2 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0082/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 83. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 15/2>0 squared units. At corresponding positive length scale k=4/2, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation30/1

Multiply the given positive area by k² to obtain 30/1 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0083/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 84. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 17/2>0 squared units. At corresponding positive length scale k=1/3, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation17/18

Multiply the given positive area by k² to obtain 17/18 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0084/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 85. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 19/2>0 squared units. At corresponding positive length scale k=2/1, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation38/1

Multiply the given positive area by k² to obtain 38/1 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0085/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 86. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 21/2>0 squared units. At corresponding positive length scale k=3/2, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation189/8

Multiply the given positive area by k² to obtain 189/8 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0086/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 87. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 23/2>0 squared units. At corresponding positive length scale k=4/3, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation184/9

Multiply the given positive area by k² to obtain 184/9 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0087/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 88. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 25/2>0 squared units. At corresponding positive length scale k=1/1, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation25/2

Multiply the given positive area by k² to obtain 25/2 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0088/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 89. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 27/2>0 squared units. At corresponding positive length scale k=2/2, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation27/2

Multiply the given positive area by k² to obtain 27/2 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0089/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 90. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 29/2>0 squared units. At corresponding positive length scale k=3/3, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation29/2

Multiply the given positive area by k² to obtain 29/2 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0090/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 91. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 31/2>0 squared units. At corresponding positive length scale k=4/1, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation248/1

Multiply the given positive area by k² to obtain 248/1 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0091/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 92. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 33/2>0 squared units. At corresponding positive length scale k=1/2, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation33/8

Multiply the given positive area by k² to obtain 33/8 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0092/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 93. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 35/2>0 squared units. At corresponding positive length scale k=2/3, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation70/9

Multiply the given positive area by k² to obtain 70/9 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0093/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 94. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 37/2>0 squared units. At corresponding positive length scale k=3/1, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation333/2

Multiply the given positive area by k² to obtain 333/2 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0094/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 95. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 39/2>0 squared units. At corresponding positive length scale k=4/2, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation78/1

Multiply the given positive area by k² to obtain 78/1 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0095/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 96. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 41/2>0 squared units. At corresponding positive length scale k=1/3, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation41/18

Multiply the given positive area by k² to obtain 41/18 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0096/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 97. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 43/2>0 squared units. At corresponding positive length scale k=2/1, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation86/1

Multiply the given positive area by k² to obtain 86/1 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0097/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 98. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 45/2>0 squared units. At corresponding positive length scale k=3/2, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation405/8

Multiply the given positive area by k² to obtain 405/8 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0098/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 99. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 47/2>0 squared units. At corresponding positive length scale k=4/3, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation376/9

Multiply the given positive area by k² to obtain 376/9 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0099/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate





## 100. Conditional Scaling of a Given Positive Area

Use one equal-unit orthonormal Euclidean Cartesian frame. A nondegenerate triangle has given area 49/2>0 squared units. At corresponding positive length scale k=1/1, find the conditional scaled area. Give a reduced fraction with positive denominator, retaining /1 for integers.

View answer and explanation49/2

Multiply the given positive area by k² to obtain 49/2 squared units. Do not recompute a triangle area from coordinates, inherit rectangle-area Evidence, or claim general measure theory.



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261006-advance-20261007-r06-similarity-0100/)

Labeled triangle similarity with a specified positive scale · qf-similarity-scaled-area · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261006-advance-20261007-r06-similarity-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261006-advance-20261007-r06-similarity-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261006-advance-20261007-r06-similarity-foundations/validation-report.json)