What Congruence Gives
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 9 of 63.
Once two triangles are known to be congruent, every pair of matching parts is equal: three pairs of sides and three pairs of angles. In a proof this rule has a short name, CPCTC: corresponding parts of congruent triangles are congruent. "Corresponding" is the textbook word for matching.
| Statement | Reason |
|---|---|
| 1. △PQR ≅ △XYZ | Given |
| 2. ∠QRP = ∠YZX | CPCTC, using line 1 |
CPCTC always cites the line that says the triangles are congruent, because that is where the matching comes from. Most proofs in this section end this way: first show two triangles are congruent, then read off the part you want.
Challenge
You are given △ABC ≅ △EFD. Prove that BC = FD: write the given, then the side pair with its reason, then press Check.
Try it yourself
Write the proof
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Congruence & Proof
1What a Proof Is
Given and ProveStatements and ReasonsChaining Equal PartsYour First Full ProofRecap: A Chain of Reasons2Congruent Triangles
Same Size, Same ShapeMatching SidesMatching AnglesWhat Congruence GivesRecap: Matching Parts8Proofs with Vertical Angles
Vertical Angles in ProofsThe BowtieBowtie with ASALinear Pairs in ProofsRecap: Vertical Angles