Question

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

Explanation:

Step1: Use the AA (Angle - Angle) similarity criterion

In \(\triangle PRQ\) and \(\triangle PSR\), we know that \(\angle QPR=\angle RPS\) (given as the same angle at vertex \(P\)). Also, \(\angle PRQ = \angle PSR\) (right - angle and another angle relation).
Since two angles of \(\triangle PRQ\) are equal to two angles of \(\triangle PSR\), by the AA similarity criterion, the two triangles are similar.

Answer:

\(\triangle PRQ\) is similar to \(\triangle PSR\)