Question

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

Explanation:

Step1: Identify given congruent sides

We know $\overline{PQ} \cong \overline{TS}$ (marked by congruent arrows).

Step2: Identify vertical angles

$\angle PRQ$ and $\angle TRS$ are vertical angles, so $\angle PRQ = \angle TRS$.

Step3: Evaluate similarity criteria

We only have one pair of congruent sides and one pair of congruent angles, but the angle is not the included angle between two sides (SAS similarity requires the angle between two proportional sides), and we have no information about other angles or side proportions. We cannot satisfy AA, SAS, or SSS similarity criteria with the given data.

Answer:

There is not enough information to determine whether the triangles are similar.