Given triangle LMN and triangle VTU, how might the AA Similarity Theorem be used to prove triangle LMN ~ triangle VTU?

Question

a. Show LM : VT = MN : TU
b. Show ∠L + ∠V + ∠N = ∠V + ∠T + ∠U = 180 degrees
c. Show ∠L ≅ ∠V and ∠M ≅ ∠U
d. Show ∠L ≅ ∠V and ∠M ≅ ∠T

Answer 1

The AA Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. To prove triangle LMN ~ triangle VTU using the AA Similarity Theorem, you would focus on showing that two pairs of corresponding angles are congruent.

Among the options you provided, the correct approach is:

c. Show ∠L ≅ ∠V and ∠M ≅ ∠U

By demonstrating that these angles are congruent, you would satisfy the criteria of the AA Similarity Theorem, leading to the conclusion that triangle LMN is similar to triangle VTU (LMN ~ VTU).