Question

using a compass and a straightedge. $overline{qs}$ is constructed in $\triangle pqr$ as shown. which statement is true? a) $angle pqscongangle rqs$ b) $angle rqscongangle qpr$ c) $overline{qs}congoverline{pq}$ d) $overline{qs}congoverline{ps}$

Explanation:

Step1: Recall angle - bisector construction

When a compass and straight - edge are used to construct a line segment like $\overline{QS}$ in a triangle as shown, the construction is of an angle bisector. An angle bisector divides an angle into two congruent angles.

Step2: Identify the bisected angle

In $\triangle PQR$, $\overline{QS}$ is constructed as an angle bisector of $\angle PQR$. So, $\angle PQS\cong\angle RQS$.

Answer:

A. $\angle PQS\cong\angle RQS$