Question

select the correct answer.
which triangles are congruent according to the sas criterion?
a. △abc and △lmn
b. △lmn and △fge
c. △lmn, △fge, and △pqr
d. △lmn and △pqr
e. △abc, △fge, and △pqr

Explanation:

Step1: Recall SAS criterion

SAS (Side - Angle - Side) criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze each option

• For option A: $\triangle ABC$ and $\triangle LMN$: The sides and included angles do not match as per the figure.
• For option B: $\triangle LMN$ and $\triangle FGE$: The sides and included angles do not match as per the figure.
• For option C: $\triangle LMN,\triangle FGE$ and $\triangle PQR$: The sides and included angles do not match as per the figure.
• For option D: In $\triangle LMN$ and $\triangle PQR$
• Let's assume the marked equal sides. If we consider the two sides (marked with one and two ticks respectively) and the included angle (marked with a curve) of $\triangle LMN$ and $\triangle PQR$, we can see that two sides and the included angle of $\triangle LMN$ are equal to two sides and the included angle of $\triangle PQR$.
• For option E: $\triangle ABC,\triangle FGE$ and $\triangle PQR$: The sides and included angles do not match as per the figure.

Answer:

D. $\triangle LMN$ and $\triangle PQR$