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Write a triangle proof, step by step

The congruence and similarity proof sheets hide one reason and let a child choose it.

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The question
PQRS

Given PQ ≅ PS; RQ ≅ RS

Prove △PQR ≅ △PSR

StatementsReasons
1.
2.
3.
4.

Prove △PQR ≅ △PSR

Prove:△PQR ≅ △PSR
1. PQ ≅ PS→Given
2. RQ ≅ RS→Given
3. PR ≅ PR→Reflexive Property
4. △PQR ≅ △PSR→SSS
  1. You are given PQ ≅ PS; RQ ≅ RS, and you have to prove △PQR ≅ △PSR. Build it one line at a time — each line is a statement and the reason it is true.
  2. 1. PQ ≅ PS — This fact is handed to you in the Given — nothing has to justify it.
  3. 2. RQ ≅ RS — This fact is handed to you in the Given — nothing has to justify it.
  4. 3. PR ≅ PR — A segment (or angle) is congruent to itself. The two triangles share this side, so it is equal in both by the reflexive property.
  5. 4. △PQR ≅ △PSR — Three pairs of sides are now known equal, and three sides fix a triangle: SSS.
  6. That is the whole proof: the last line, △PQR ≅ △PSR, follows by SSS.

How it works.

  1. 01

    You are given PQ ≅ PS; RQ ≅ RS, and you have to prove △PQR ≅ △PSR. Build it one line at a time — each line is a statement and the reason it is true.

  2. 02

    1. PQ ≅ PS — This fact is handed to you in the Given — nothing has to justify it.

  3. 03

    2. RQ ≅ RS — This fact is handed to you in the Given — nothing has to justify it.

  4. 04

    3. PR ≅ PR — A segment (or angle) is congruent to itself. The two triangles share this side, so it is equal in both by the reflexive property.

  5. 05

    4. △PQR ≅ △PSR — Three pairs of sides are now known equal, and three sides fix a triangle: SSS.

  6. 06

    That is the whole proof: the last line, △PQR ≅ △PSR, follows by SSS.

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