Write a triangle proof
The question
Given PQ ≅ PS; RQ ≅ RS
Prove △PQR ≅ △PSR
| Statements | Reasons |
|---|---|
| 1. | |
| 2. | |
| 3. | |
| 4. |
Prove △PQR ≅ △PSR
How it works.
Prove:△PQR ≅ △PSR
1. PQ ≅ PS→Given
2. RQ ≅ RS→Given
3. PR ≅ PR→Reflexive Property
4. △PQR ≅ △PSR→SSS
- 01
You are given PQ ≅ PS; RQ ≅ RS, and you have to prove △PQR ≅ △PSR. Each line is a statement and the reason it is true.
- 02
1. PQ ≅ PS — It is given.
- 03
2. RQ ≅ RS — It is given.
- 04
3. PR ≅ PR — The two triangles share this side, and anything is congruent to itself.
- 05
4. △PQR ≅ △PSR — All three pairs of sides are equal: SSS.
- 06
△PQR ≅ △PSR by SSS — proved.