Question

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

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze the given triangles \(\triangle TSR\) and \(\triangle QRS\)

We are given that \(TS = QR=5\) in and \(\angle TSR=\angle QRS = 66^{\circ}\). Also, \(SR\) is a common side. By the reflexive property of congruence, \(SR\cong SR\).
So, in \(\triangle TSR\) and \(\triangle QRS\), we have \(TS = QR\), \(\angle TSR=\angle QRS\) and \(SR = SR\) (by reflexive property).

Answer:

yes, because along with the given information on the diagram, \(SR\cong RS\) by the reflexive property.