Question

Prove that triangles KNM and MLK are congruent using the AAS congruence theorem. Given that the two triangles share a common side KM, and angles KLM and KNM are marked with a single arc, while angles NKM and LMK are marked with a double arc.

Answer 1

To prove that triangles KNM and MLK are congruent using the AAS congruence theorem, we need to show that they have two pairs of corresponding congruent angles and a pair of corresponding congruent sides.

Step-by-step explanation:

To prove that triangles KNM and MLK are congruent using the AAS congruence theorem, we need to show that they have two pairs of corresponding congruent angles and a pair of corresponding congruent sides. Here are the steps:

1. Given that angle KLM and angle KNM are marked with a single arc, we know that they are congruent by the definition of congruent angles.
2. Similarly, given that angle NKM and angle LMK are marked with a double arc, we know that they are congruent.
3. Since the two triangles share a common side KM, we have a pair of corresponding congruent sides.
4. Therefore, by the AAS congruence theorem, triangles KNM and MLK are congruent.