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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-20260925-triangle-object-language · 2026-09-25 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
The three points in order are A, A, C; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
No
The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are D, E, F; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are G, H, I; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are J, K, L; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are M, M, P; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
No
The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are Q, R, S; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
No
The vertices are distinct but collinear, so they do not form the nondegenerate triangle of this entry.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are T, U, V; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are W, X, Y; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are A, A, D; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
No
The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are A, C, E; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are B, D, F; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
No
The vertices are distinct but collinear, so they do not form the nondegenerate triangle of this entry.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are C, E, G; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are D, D, H; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
No
The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are E, G, I; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are F, H, J; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are G, I, K; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
No
The vertices are distinct but collinear, so they do not form the nondegenerate triangle of this entry.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are H, H, L; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
No
The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are I, K, M; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are J, L, N; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are K, M, O; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are L, L, P; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
No
The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are M, O, Q; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are N, P, R; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are O, Q, S; the prompt explicitly states that they are noncollinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
Yes
The three vertices are distinct and noncollinear, so they form a nondegenerate triangle.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
The three points in order are P, P, T; the prompt explicitly states that they are collinear. Using only the distinctness and noncollinearity conditions, do they form a nondegenerate triangle?
No
The vertices are not all distinct, so they do not form the nondegenerate triangle of this entry.
Reviewed step-by-step derivation
Triangle · qf-triangle-explicit-validity · candidate
Triangle ABC has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{A, B, C}
Taking the three labels and sorting them canonically gives {A, B, C}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle DEF has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{D, E, F}
Taking the three labels and sorting them canonically gives {D, E, F}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle GHI has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{G, H, I}
Taking the three labels and sorting them canonically gives {G, H, I}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle JKL has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{J, K, L}
Taking the three labels and sorting them canonically gives {J, K, L}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle MNP has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{M, N, P}
Taking the three labels and sorting them canonically gives {M, N, P}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle QRS has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{Q, R, S}
Taking the three labels and sorting them canonically gives {Q, R, S}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle TUV has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{T, U, V}
Taking the three labels and sorting them canonically gives {T, U, V}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle WXY has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{W, X, Y}
Taking the three labels and sorting them canonically gives {W, X, Y}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle ABD has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{A, B, D}
Taking the three labels and sorting them canonically gives {A, B, D}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle ACE has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{A, C, E}
Taking the three labels and sorting them canonically gives {A, C, E}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle BDF has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{B, D, F}
Taking the three labels and sorting them canonically gives {B, D, F}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle CEG has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{C, E, G}
Taking the three labels and sorting them canonically gives {C, E, G}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle DFH has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{D, F, H}
Taking the three labels and sorting them canonically gives {D, F, H}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle EGI has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{E, G, I}
Taking the three labels and sorting them canonically gives {E, G, I}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle FHJ has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{F, H, J}
Taking the three labels and sorting them canonically gives {F, H, J}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle GIK has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{G, I, K}
Taking the three labels and sorting them canonically gives {G, I, K}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle HJL has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{H, J, L}
Taking the three labels and sorting them canonically gives {H, J, L}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle IKM has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{I, K, M}
Taking the three labels and sorting them canonically gives {I, K, M}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle JLN has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{J, L, N}
Taking the three labels and sorting them canonically gives {J, L, N}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle KMO has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{K, M, O}
Taking the three labels and sorting them canonically gives {K, M, O}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle LNP has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{L, N, P}
Taking the three labels and sorting them canonically gives {L, N, P}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle MOQ has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{M, O, Q}
Taking the three labels and sorting them canonically gives {M, O, Q}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle NPR has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{N, P, R}
Taking the three labels and sorting them canonically gives {N, P, R}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle OQS has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{O, Q, S}
Taking the three labels and sorting them canonically gives {O, Q, S}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle PRT has explicitly distinct noncollinear vertices. Write its vertex set in canonical order.
{P, R, T}
Taking the three labels and sorting them canonically gives {P, R, T}.
Reviewed step-by-step derivation
Triangle · qf-triangle-vertex-set · candidate
Triangle ABC has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
AB, AC, BC
Pairwise connection of the vertices followed by canonical ordering gives AB, AC, BC.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle DEF has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
DE, DF, EF
Pairwise connection of the vertices followed by canonical ordering gives DE, DF, EF.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle GHI has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
GH, GI, HI
Pairwise connection of the vertices followed by canonical ordering gives GH, GI, HI.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle JKL has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
JK, JL, KL
Pairwise connection of the vertices followed by canonical ordering gives JK, JL, KL.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle MNP has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
MN, MP, NP
Pairwise connection of the vertices followed by canonical ordering gives MN, MP, NP.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle QRS has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
QR, QS, RS
Pairwise connection of the vertices followed by canonical ordering gives QR, QS, RS.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle TUV has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
TU, TV, UV
Pairwise connection of the vertices followed by canonical ordering gives TU, TV, UV.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle WXY has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
WX, WY, XY
Pairwise connection of the vertices followed by canonical ordering gives WX, WY, XY.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle ABD has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
AB, AD, BD
Pairwise connection of the vertices followed by canonical ordering gives AB, AD, BD.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle ACE has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
AC, AE, CE
Pairwise connection of the vertices followed by canonical ordering gives AC, AE, CE.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle BDF has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
BD, BF, DF
Pairwise connection of the vertices followed by canonical ordering gives BD, BF, DF.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle CEG has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
CE, CG, EG
Pairwise connection of the vertices followed by canonical ordering gives CE, CG, EG.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle DFH has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
DF, DH, FH
Pairwise connection of the vertices followed by canonical ordering gives DF, DH, FH.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle EGI has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
EG, EI, GI
Pairwise connection of the vertices followed by canonical ordering gives EG, EI, GI.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle FHJ has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
FH, FJ, HJ
Pairwise connection of the vertices followed by canonical ordering gives FH, FJ, HJ.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle GIK has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
GI, GK, IK
Pairwise connection of the vertices followed by canonical ordering gives GI, GK, IK.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle HJL has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
HJ, HL, JL
Pairwise connection of the vertices followed by canonical ordering gives HJ, HL, JL.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle IKM has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
IK, IM, KM
Pairwise connection of the vertices followed by canonical ordering gives IK, IM, KM.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle JLN has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
JL, JN, LN
Pairwise connection of the vertices followed by canonical ordering gives JL, JN, LN.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle KMO has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
KM, KO, MO
Pairwise connection of the vertices followed by canonical ordering gives KM, KO, MO.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle LNP has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
LN, LP, NP
Pairwise connection of the vertices followed by canonical ordering gives LN, LP, NP.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle MOQ has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
MO, MQ, OQ
Pairwise connection of the vertices followed by canonical ordering gives MO, MQ, OQ.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle NPR has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
NP, NR, PR
Pairwise connection of the vertices followed by canonical ordering gives NP, NR, PR.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle OQS has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
OQ, OS, QS
Pairwise connection of the vertices followed by canonical ordering gives OQ, OS, QS.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle PRT has explicitly distinct noncollinear vertices. List its three undirected sides in canonical order.
PR, PT, RT
Pairwise connection of the vertices followed by canonical ordering gives PR, PT, RT.
Reviewed step-by-step derivation
Triangle · qf-triangle-side-set · candidate
Triangle ABC has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex A?
BC
Removing vertex A leaves the other two vertices, which form side BC.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle DEF has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex E?
DF
Removing vertex E leaves the other two vertices, which form side DF.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle GHI has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex I?
GH
Removing vertex I leaves the other two vertices, which form side GH.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle JKL has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex J?
KL
Removing vertex J leaves the other two vertices, which form side KL.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle MNP has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex N?
MP
Removing vertex N leaves the other two vertices, which form side MP.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle QRS has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex S?
QR
Removing vertex S leaves the other two vertices, which form side QR.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle TUV has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex T?
UV
Removing vertex T leaves the other two vertices, which form side UV.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle WXY has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex X?
WY
Removing vertex X leaves the other two vertices, which form side WY.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle ABD has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex D?
AB
Removing vertex D leaves the other two vertices, which form side AB.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle ACE has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex A?
CE
Removing vertex A leaves the other two vertices, which form side CE.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle BDF has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex D?
BF
Removing vertex D leaves the other two vertices, which form side BF.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle CEG has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex G?
CE
Removing vertex G leaves the other two vertices, which form side CE.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle DFH has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex D?
FH
Removing vertex D leaves the other two vertices, which form side FH.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle EGI has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex G?
EI
Removing vertex G leaves the other two vertices, which form side EI.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle FHJ has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex J?
FH
Removing vertex J leaves the other two vertices, which form side FH.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle GIK has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex G?
IK
Removing vertex G leaves the other two vertices, which form side IK.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle HJL has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex J?
HL
Removing vertex J leaves the other two vertices, which form side HL.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle IKM has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex M?
IK
Removing vertex M leaves the other two vertices, which form side IK.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle JLN has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex J?
LN
Removing vertex J leaves the other two vertices, which form side LN.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle KMO has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex M?
KO
Removing vertex M leaves the other two vertices, which form side KO.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle LNP has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex P?
LN
Removing vertex P leaves the other two vertices, which form side LN.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle MOQ has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex M?
OQ
Removing vertex M leaves the other two vertices, which form side OQ.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle NPR has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex P?
NR
Removing vertex P leaves the other two vertices, which form side NR.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle OQS has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex S?
OQ
Removing vertex S leaves the other two vertices, which form side OQ.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Triangle PRT has explicitly distinct noncollinear vertices. Which undirected side is opposite vertex P?
RT
Removing vertex P leaves the other two vertices, which form side RT.
Reviewed step-by-step derivation
Triangle · qf-triangle-opposite-side · candidate
Canonical question JSONL · English JSONL · Validation report