Question

Given △LMN △ 𝐿 𝑀 𝑁 and △VTU △ 𝑉 𝑇 𝑈 , how might the AA Similarity Theorem be used to prove ΔLMN∼ΔVTU Δ 𝐿 𝑀 𝑁 ∼ Δ 𝑉 𝑇 𝑈 ?(1 point) Responses Show ∠L≅∠V ∠ 𝐿 ≅ ∠ 𝑉 and ∠M≅∠U ∠ 𝑀 ≅ ∠ 𝑈 . Show angle liters is congruent to angle cap v and angle cap m is congruent to angle cap u . Show ∡L+∡M+∡N=∡V+∡T+∡U=180° ∡ 𝐿 + ∡ 𝑀 + ∡ 𝑁 = ∡ 𝑉 + ∡ 𝑇 + ∡ 𝑈 = 180 ° . Show measure of angle L plus measure of angle cap m plus measure of angle cap n is equal to measure of angle cap v plus measure of angle cap t plus measure of angle cap u is equal to 180 degrees . Show ∠L≅∠V ∠ 𝐿 ≅ ∠ 𝑉 and ∠M≅∠T ∠ 𝑀 ≅ ∠ 𝑇 . Show angle cap L is congruent to angle cap v and angle cap m is congruent to angle cap t . Show LM¯¯¯¯¯¯¯¯¯:VT¯¯¯¯¯¯¯=MN¯¯¯¯¯¯¯¯¯¯:TU¯¯¯¯¯¯¯ 𝐿 𝑀 ¯ : 𝑉 𝑇 ¯ = 𝑀 𝑁 ¯ : 𝑇 𝑈 ¯

Answer 1

Use the correspondence L↔V, M↔T, N↔U. Show two pairs of corresponding angles are congruent:

1. ∠L ≅ ∠V
2. ∠M ≅ ∠T

By the AA (Angle–Angle) Similarity Theorem, ΔLMN ∼ ΔVTU. Hence corresponding sides are proportional:
LM/VT = MN/TU = LN/VU.