Question

Determine whether the triangles must be congruent. If so, name the postulate or theojem that best justifies youranswer. If not, explain.Choose the correct answer below.A. The triangles are congruent by SAS.B. The triangles are congruent by ASA.C. The triangles are congruent by AAS.D. The triangles are congruent by SSS.

Answer 1

In the figure, the two triangles are:

$\Delta\text{MNP and }\Delta\text{MQP}$

In these triangles, it follows:

$\begin{gathered} \angle NMP\cong\angle QMP \\ \angle MNP\cong\angle MQP \\ MP\cong MP \end{gathered}$

Hence the triangles are congruent by AAS test.

Option C is correct.