Question

△prs ≅ △qsr. complete the proof that ∠prq ≅ ∠psq.

Explanation:

Step1: Identify the triangles for the angles

We need to use the triangles \(\triangle PRQ\) and \(\triangle QSP\).

Step2: Use the SSS (Side - Side - Side) congruence criterion

Since \(\overline{PS}\cong\overline{QR}\), \(\overline{PR}\cong\overline{QS}\), and \(\overline{PQ}\cong\overline{QP}\) (common side).
By SSS congruence, \(\triangle PRQ\cong\triangle QSP\).

Step3: Use CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

For \(\triangle PRQ\cong\triangle QSP\), the corresponding angles \(\angle PRQ\) and \(\angle PSQ\) are congruent.

Answer:

1. \(\triangle PRQ\cong\triangle QSP\) (by SSS: \(\overline{PS}\cong\overline{QR}\), \(\overline{PR}\cong\overline{QS}\), \(\overline{PQ}\cong\overline{QP}\)); \(\angle PRQ\cong\angle PSQ\) (by CPCTC)