Question

1. are these triangles congruent? if so, state the rule which you used to determine congruence. a) aaa b) not necessarily congruent c) asa d) aas 8. are these triangles congruent? if so, state the rule which you used to determine congruence. a) asa b) aas c) ssa d) not necessarily congruent 9. are these triangles congruent? if so, state the rule which you used to determine congruence. asa

Explanation:

Step1: Recall triangle congruence rules

The AAS (Angle - Angle - Side) rule states that if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, then the triangles are congruent.
In triangle \(LMN\) and \(RQP\), \(\angle L = 45^{\circ}\), \(\angle M=110^{\circ}\), \(LN = 12m\) and \(\angle P = 45^{\circ}\), \(\angle Q = 110^{\circ}\), \(RQ=12m\).

Step2: Apply the AAS rule

We have two angles (\(\angle L=\angle P = 45^{\circ}\) and \(\angle M=\angle Q = 110^{\circ}\)) and a non - included side (\(LN = RQ=12m\)) equal.

Answer:

d) AAS