Chaining Equal Parts
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 3 of 63.
Two facts that share a part can be joined. If AB = CD and CD = EF, then AB = EF: both are equal to CD, so they are equal to each other. This is the Transitive property, and it works for angles as well as sides.
| Statement | Reason |
|---|---|
| 1. AB = CD | Given |
| 2. CD = EF | Given |
| 3. AB = EF | Transitive property, using lines 1 and 2 |
Chaining is how a proof travels. One rule takes you from the first part to a middle part, another from the middle part to the last one, and the transitive property closes the chain. The line that does it must cite both links.
Challenge
The arcs say ∠1 = ∠2, and ∠2 and ∠3 are vertical angles. The first two lines are written for you. Add the line that proves ∠1 = ∠3, 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