Question

tu ≅ qr, pq ≅ rs, and pu ≅ st. complete the proof that ∠s ≅ ∠p.

Explanation:

Step1: Prove triangles congruent

Since \( \overline{TU}\cong\overline{QR}\), \( \overline{PQ}\cong\overline{RS}\), and \( \overline{PU}\cong\overline{ST}\), and from steps 4 - 7 we have \( RT = QU\). By the Side - Side - Side (SSS) congruence criterion, \( \triangle PQU\cong\triangle SRT\).

Step2: Use congruent triangles property

If two triangles are congruent, then their corresponding angles are congruent. So, \( \angle S\cong\angle P\) (Corresponding Parts of Congruent Triangles are Congruent - CPCTC).

Answer:

Statement: \( \triangle PQU\cong\triangle SRT\); Reason: SSS Congruence Criterion
Statement: \( \angle S\cong\angle P\); Reason: CPCTC