Write a similarity proof
The question
Given ∠ADE ≅ ∠B
Prove △ADE ~ △ABC
| Statements | Reasons |
|---|---|
| 1. | |
| 2. | |
| 3. |
Prove △ADE ~ △ABC
How it works.
Prove:△ADE ~ △ABC
1. ∠A ≅ ∠A→Reflexive Property
2. ∠ADE ≅ ∠B→Given
3. △ADE ~ △ABC→AA ~
- 01
You are given ∠ADE ≅ ∠B, and you have to prove △ADE ~ △ABC. Each line is a statement and the reason it is true.
- 02
1. ∠A ≅ ∠A — The two triangles share this side, and anything is congruent to itself.
- 03
2. ∠ADE ≅ ∠B — It is given.
- 04
3. △ADE ~ △ABC — Two pairs of angles are congruent, and that is enough for similar triangles: AA.
- 05
△ADE ~ △ABC by AA ~ — proved.