Question

triangle congruence: sas determining if triangles are congruent can \\( \triangle tsr \\) and \\( \triangle qrs \\) be proven congruent by sas? yes, because a reflection will map \\( \triangle tsr \\) onto \\( \triangle qrs \\) yes, because along with the given information on the diagram, \\( \overline{sr} \cong \overline{rs} \\) by the reflexive property yes, because p appears to be the midpoint of \\( \overline{sq} \\) and \\( \overline{tr} \\) no, because not enough information given to prove the triangles congruent by sas

Explanation:

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

For two triangles to be congruent by SAS, two sides and the included angle of one triangle must be equal to the corresponding two sides and the included angle of the other triangle.

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

• We are given \(TS = QR=5\) inches.
• We are given \( \angle T = \angle Q = 66^{\circ}\).
• For the SAS criterion, the included side between the given angles should be considered. By the reflexive property \(SR = RS\).

Answer:

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