Question

can δtsr and δqrs be proven congruent by sas? yes, because along with the given information on the diagram, sr ≅ rs by the reflexive property yes, because a reflection will map δtsr onto δqrs yes, because p appears to be the midpoint of sq and tr no, because not enough is information given to prove the triangles congruent by sas

Explanation:

Step1: Recall SAS congruence criterion

SAS (Side - Angle - Side) requires two pairs of congruent sides and the included angle between them to be congruent.

Step2: Identify given information

We are given that $\angle TSR = 66^{\circ}$, $TS = 5$ in, $\angle QRS=66^{\circ}$, $QR = 5$ in, and side $SR$ is common to both $\triangle TSR$ and $\triangle QRS$. By the reflexive property, $SR\cong RS$.

Step3: Check SAS criterion

We have $TS\cong QR$ (both are 5 in), $\angle TSR\cong\angle QRS$ (both are $66^{\circ}$) and $SR\cong RS$. The angle is the included angle between the two pairs of congruent sides. So, $\triangle TSR$ and $\triangle QRS$ are congruent by SAS.

Answer:

A. yes, because along with the given information on the diagram, $\overline{SR}\cong\overline{RS}$ by the reflexive property