Answer:
Correct answer is:
D) ΔHLK ≅ ΔHMN by AAS; ∠K ≅ ∠N because they're corresponding angles in congruent triangles.
Step-by-step explanation:
We are given the diagram, in which there are 2 triangles namely [tex]\triangle HLK, \triangle HMN[/tex].
1. Side KH = Side NH
2. [tex]\angle L \cong \angle M[/tex]
From the given figure, we can derive that:
[tex]\angle KHL \cong \angle NHM[/tex]
Property used: Vertically opposite angels made by two lines crossing each other are equal.
So, we have two angles ([tex]\angle L \cong \angle M[/tex] and [tex]\angle KHL \cong \angle NHM[/tex])of the triangle as same and one side equal from the two given triangles [tex]\triangle HLK, \triangle HMN[/tex].
So, we can say that the two triangles are congruent.
[tex]\triangle HLK \cong \triangle HMN[/tex]
The side is not between the two equal angles, so it is AAS congruence.
And Congruent triangles have their corresponding angles equal.
Therefore, option D) is true :
ΔHLK ≅ ΔHMN by AAS; ∠K ≅ ∠N, because they're corresponding angles in congruent triangles.
