Question

if $overline{ps}congoverline{rs}$ and $qr = 64$, what is $pq?
pq=square$

Explanation:

Step1: Identify congruent triangles

Since $\overline{PS}\cong\overline{RS}$ and $\angle PSQ=\angle RSQ = 90^{\circ}$ (right - angle shown) and $\overline{SQ}=\overline{SQ}$ (common side), by the Hypotenuse - Leg (HL) congruence criterion in right - triangles $\triangle PQS\cong\triangle RQS$.

Step2: Use the property of congruent triangles

For congruent triangles $\triangle PQS$ and $\triangle RQS$, corresponding sides are equal. So, $PQ = QR$.

Answer:

64