Question

problem 15: from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: △pqr and ∠p ≅ ∠q prove: (overline{pr}congoverline{rq})

Explanation:

Step1: Identify given information

Given \(\triangle PQR\) and \(\angle P\cong\angle Q\).

Step2: Recall relevant theorem

The Isosceles - Triangle Theorem states that if two angles of a triangle are congruent, the sides opposite them are congruent.

Step3: Apply theorem

Since \(\angle P\) and \(\angle Q\) are congruent, the sides opposite them (\(\overline{PR}\) and \(\overline{RQ}\)) are congruent, i.e., \(\overline{PR}\cong\overline{RQ}\).

Answer:

The Isosceles - Triangle Theorem (not shown in options but correct justification). If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Since in \(\triangle PQR\), \(\angle P\cong\angle Q\), by the Isosceles - Triangle Theorem, \(\overline{PR}\cong\overline{RQ}\).