Question

triangle rst and triangle pqt are drawn below. if $overline{rs}congoverline{pq}$, $overline{rt}congoverline{pt}$, and $angle rcongangle p$, use the dropdown boxes below to determine a transformation that maps triangle rst onto triangle pqt. then use a congruence statement to explain why this is possible.

Explanation:

Step1: Identify congruence criterion

Given $\overline{RS}\cong\overline{PQ}$, $\overline{RT}\cong\overline{PT}$, and $\angle R\cong\angle P$. By the Side - Angle - Side (SAS) congruence criterion, $\triangle RST\cong\triangle PQT$.

Step2: Determine transformation

A rotation about point $T$ can map $\triangle RST$ onto $\triangle PQT$. Since the two triangles are congruent (by SAS), we can rotate $\triangle RST$ around point $T$ so that the corresponding sides and angles coincide.

Answer:

A rotation about point $T$; $\triangle RST\cong\triangle PQT$ by the SAS congruence criterion.