Transitive Property of Equality Variation 2
Similar Triangles

Proof: Similar Triangles Theorem

Let's prove the following theorem:

if m∠CAB = m∠ZXY and m∠ABC = m∠XYZ, then △ABC ∼ △XYZ

A B C X Y Z X Y Z L M N

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 m∠CAB = m∠ZXY
2 m∠ABC = m∠XYZ
Additional Assumptions
3 △ABC ∼ △LMN
4 distance LM = distance XY
Proof Table
# Claim Reason
1 m∠CAB = m∠NLM if △ABC ∼ △LMN, then m∠CAB = m∠NLM
2 m∠ABC = m∠LMN if △ABC ∼ △LMN, then m∠ABC = m∠LMN
3 m∠NLM = m∠ZXY if m∠CAB = m∠NLM and m∠CAB = m∠ZXY, then m∠NLM = m∠ZXY
4 m∠LMN = m∠XYZ if m∠ABC = m∠LMN and m∠ABC = m∠XYZ, then m∠LMN = m∠XYZ
5 △NLM ≅ △ZXY if m∠NLM = m∠ZXY and distance LM = distance XY and m∠LMN = m∠XYZ, then △NLM ≅ △ZXY
6 △LMN ≅ △XYZ if △NLM ≅ △ZXY, then △LMN ≅ △XYZ
7 △LMN ∼ △XYZ if △LMN ≅ △XYZ, then △LMN ∼ △XYZ
8 △ABC ∼ △XYZ if △ABC ∼ △LMN and △LMN ∼ △XYZ, then △ABC ∼ △XYZ
Previous Lesson

Comments

Please log in to add comments