Question

if \\( \angle p r q \cong \angle p r s \\) and \\( p s = 14 \\), what is \\( p q \\)?

Explanation:

Step1: Apply the Angle - Angle - Side (AAS) Congruence Theorem

Since \(\angle PQR=\angle PSR = 90^{\circ}\) (right angles), \(\angle PRQ\cong\angle PRS\) (given), and \(PR = PR\) (common side). By AAS congruence, \(\triangle PQR\cong\triangle PSR\).

Step2: Use the property of congruent triangles

If two triangles \(\triangle PQR\) and \(\triangle PSR\) are congruent, then their corresponding sides are equal. That is \(PQ = PS\).

Answer:

\(14\)