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Use CPCTC to prove parts of triangles are congruent.

Learn how to use CPCTC to prove corresponding parts of congruent triangles are congruent. Explore examples and step-by-step proofs. Enhance your triangle congruence skills now!

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Use CPCTC to prove parts of triangles are congruent.

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  1. Objective Use CPCTC to prove parts of triangles are congruent.

  2. Vocabulary CPCTC

  3. _________is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification in a proof after you have proven two triangles congruent.

  4. Remember! SSS, SAS, ASA, AAS, and HL use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent.

  5. Example 1A: Engineering Application A and B are on the edges of a ravine. What is AB?

  6. Check It Out! Example 1B A landscape architect sets up the triangles shown in the figure to find the distance JK across a pond. What is JK?

  7. Given:YW bisects XZ, XY YZ. Z Example 2A: Proving Corresponding Parts Congruent Prove:XYW  ZYW

  8. Given:PR bisects QPS and QRS. Prove:PQ  PS Check It Out! Example 2B

  9. Ex.2 C Write another proof

  10. Helpful Hint Work backward when planning a proof. To show that ED || GF, look for a pair of angles that are congruent. Then look for triangles that contain these angles.

  11. Given:NO || MP, N P Prove:MN || OP Example 3A: Using CPCTC in a Proof

  12. Given:J is the midpoint of KM and NL. Prove:KL || MN Check It Out! Example 3B

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