CPCTC Proofs Worksheet

This worksheet helps grade 9 students practice CPCTC proofs in geometry, focusing on identifying congruent parts of congruent triangles.

Grade 9 Math GeometryCpctc Proofs

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3 Short AnswerFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSG.CO.B.7CCSS.MATH.CONTENT.HSG.CO.B.8

Topics

CPCTCProofsGeometryCongruent TrianglesGrade 9

7 sections · Free to use · Printable

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CPCTC Proofs Worksheet

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Read each problem carefully and provide a complete proof. Remember to state your given information, what you need to prove, and all steps with justifications. CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent'.

1. Given: AB || DC and AD || BC. Prove: ΔABC ≅ ΔCDA. Then use CPCTC to prove AB ≅ CD.

2. Given: M is the midpoint of AB and CD. Prove: ΔAMC ≅ ΔBMD. Then use CPCTC to prove AC || BD.

3. If two triangles are congruent, then their corresponding sides and corresponding angles are . This is abbreviated as .

4. To prove that two segments or angles are congruent using CPCTC, you must first prove that the containing those parts are .

5. CPCTC can be used as the first step in a geometric proof.

True

False

6. If ΔXYZ ≅ ΔPQR, then ∠Y ≅ ∠Q by CPCTC.

True

False

7. Given: AC ≅ BD and AB || CD. Prove: AD || BC.