Question

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

Explanation:

Step1: Identify vertical angles

$\angle PRQ = \angle SRT$ (vertical angles are congruent)

Step2: Find $\angle PRQ$ sum

In $\triangle PRQ$, $\angle P + 98^\circ + \angle PRQ = 180^\circ$

Step3: Find $\angle SRT$ sum

In $\triangle TRS$, $\angle S + 53^\circ + \angle SRT = 180^\circ$

Step4: Compare angle sets

Substitute $\angle PRQ = \angle SRT$: $\angle P + 98^\circ = \angle S + 53^\circ$, so $\angle P = \angle S - 45^\circ$. No matching angle pairs to satisfy AA similarity.

Answer:

$\triangle PRQ$ is not similar to $\triangle TRS$.