Question

given that nm = 7.
a. what congruence criteria do you use to show these two triangles are congruent?
b. write the congruence statement.
c. what is the length of the side lm using cpctc?

Explanation:

Step1: Determine congruence criteria

We have two angles and a non - included side. For triangle congruence, the AAS (Angle - Angle - Side) criterion is used when two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of another triangle.

Step2: Write congruence statement

By AAS congruence, \(\triangle NML\cong\triangle LFG\) (corresponding vertices are matched based on angle and side correspondence).

Step3: Find length of \(LM\)

Since \(\triangle NML\cong\triangle LFG\) (by AAS), and using CPCTC (Corresponding Parts of Congruent Triangles are Congruent), \(LM = FG\). Given \(FG = 5\), so \(LM = 5\).

Answer:

A. AAS (Angle - Angle - Side)
B. \(\triangle NML\cong\triangle LFG\)
C. \(LM = 5\)