Question

Look at the figure shown below. A student made the table shown below to prove that PQ is equal to RQ 1. Provide the missing statement and justification in the proof. 2. Using complete sentences, explain why the proof would not work without the missing step.

Answer 1

1. ΔSQR ≅ ΔTQP by ASA congruence
2. triangle congruence is needed before a claim based on that can be made

Explanation:

1. The last step claims the lengths PQ and RQ are the same based on the congruence of triangles SQR and TQP. In order to make that claim, some step in the proof needs to claim that those triangles are congruent. That claim is the missing step:

ΔSQR ≅ ΔTQP --- ASA congruence postulate

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2. Without a claim of triangle congruence, the claim of triangle side congruence is unsupported. The proof must contain a claim that the triangles containing corresponding sides PQ and RQ are congruent.