Question

1. sas

a) $overline{mn}congoverline{fe}$
b) $angle lcongangle g$ or $angle ncongangle e$
c) $angle lcongangle g$
d) $angle ncongangle e$

Explanation:

Step1: Recall SAS (Side - Angle - Side) 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, the two triangles are congruent. In \(\triangle MLN\) and \(\triangle EFG\), we already know the sides are congruent (the marked segments). For SAS, we need the included angles to be congruent. The included angles for the given congruent sides are \(\angle L\) and \(\angle G\).

Step2: Analyze the options

Option A is about a side - side congruence which is not what we need for SAS. Option B gives two non - included angle possibilities which are incorrect for SAS. Option D gives a non - included angle. Option C gives the correct included angle congruence for SAS.

Answer:

C. \(\angle L\cong\angle G\)