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 \(\triangle LMN\) and \(\triangle PQR\)

• For \(\triangle LMN\) and \(\triangle PQR\):
• Let's assume the marked equal sides. Suppose \(LM = PQ\) (first side), \(LN=PR\) (second side).
• The marked equal angles: \(\angle MLN=\angle QPR\) (included angle).
• By the SAS criterion, \(\triangle LMN\cong\triangle PQR\)

Answer:

D. \(\triangle LMN\) and \(\triangle PQR\)