Question

proof prove the triangles are congruent using the aas congruence theorem.
given ∠nkm ≅ ∠lmk, ∠l ≅ ∠n
prove △nmk ≅ △lkm

1. ∠nkm ≅ ∠lmk, ∠l ≅ ∠n
2. given

2.
2.
3.
3.

Explanation:

Step1: Identify the common side

In \(\triangle NMK\) and \(\triangle LKM\), \(KM = KM\) (common side).

Step2: Apply AAS Congruence Theorem

The AAS (Angle - Angle - Side) Congruence Theorem states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
We are given \(\angle NKM\cong\angle LMK\), \(\angle L\cong\angle N\), and we have shown \(KM = KM\) (the non - included side).

Answer:

1. \(KM\cong KM\) (Common side)
2. \(\triangle NMK\cong\triangle LKM\) (AAS Congruence Theorem)