Write a similarity proof, step by step

The similar-triangle proof sheets hide one reason and let a child choose it.

The question

Given ∠ADE ≅ ∠B

Prove △ADE ~ △ABC

Prove △ADE ~ △ABC

Prove:△ADE ~ △ABC

1. ∠A ≅ ∠A→Reflexive Property

2. ∠ADE ≅ ∠B→Given

3. △ADE ~ △ABC→AA ~

You are given ∠ADE ≅ ∠B, and you have to prove △ADE ~ △ABC. Build it one line at a time — each line is a statement and the reason it is true.
1. ∠A ≅ ∠A — A segment (or angle) is congruent to itself. The two triangles share this side, so it is equal in both by the reflexive property.
2. ∠ADE ≅ ∠B — This fact is handed to you in the Given — nothing has to justify it.
3. △ADE ~ △ABC — Two pairs of angles are congruent, and two angles are enough to make triangles similar: AA.
That is the whole proof: the last line, △ADE ~ △ABC, follows by AA ~.

How it works.

01
You are given ∠ADE ≅ ∠B, and you have to prove △ADE ~ △ABC. Build it one line at a time — each line is a statement and the reason it is true.
02
1. ∠A ≅ ∠A — A segment (or angle) is congruent to itself. The two triangles share this side, so it is equal in both by the reflexive property.
03
2. ∠ADE ≅ ∠B — This fact is handed to you in the Given — nothing has to justify it.
04
3. △ADE ~ △ABC — Two pairs of angles are congruent, and two angles are enough to make triangles similar: AA.
05
That is the whole proof: the last line, △ADE ~ △ABC, follows by AA ~.