Question 35705: Triangle Validity from Explicit Conditions

Original question and givens

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?

• G001 — 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?

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-triangle

Step-by-step derivation

source roles = [qf-triangle-explicit-validity, [noncollinear, operation, vertices]]

derived = [triangle, validity, null]

source roles = [[P, P, T], No]

derived = [[P, T], No, No]

Reverse checks

• S002 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.
• S001 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.

Result

No

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.