Question

δprt and δsrq are shown below. which statement is true? δprt is similar to δsrq. δprt is not similar to δsrq. there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Recall angle - angle (AA) similarity criterion

Two triangles are similar if two pairs of corresponding angles are equal.

Step2: Identify equal angles in \(\triangle PRT\) and \(\triangle SRQ\)

In \(\triangle SRQ\), we have \(\angle R = 86^{\circ}\) and \(\angle Q=51^{\circ}\), then \(\angle S=180^{\circ}-(86^{\circ} + 51^{\circ})=43^{\circ}\). In \(\triangle PRT\), assume \(\angle R\) is common to both triangles (\(\angle R\) in \(\triangle PRT\) and \(\angle R\) in \(\triangle SRQ\)). We know one angle of \(\triangle PRT\) is \(39^{\circ}\) and the common - angle \(R = 86^{\circ}\). Since the angles of \(\triangle PRT\) and \(\triangle SRQ\) are not equal in pairs, the triangles are not similar.

Answer:

\(\triangle PRT\) is not similar to \(\triangle SRQ\)