What Congruence Gives

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 6 of 60.

△ABC ≅ △DEF says A lands on D, B on E and C on F. This one line gives you six equal pairs: three pairs of sides and three pairs of angles. You read them from the letter order. Side AB joins the 1st and 2nd corners, so it matches DE. ∠C is at the 3rd corner, so it matches ∠F.

In a proof, this rule is called CPCTC. It is short for: corresponding parts of congruent triangles are congruent. Corresponding means matching. Its line names the line that says the triangles are congruent.

Challenge

You are given △ABC ≅ △EFD. Prove that BC = FD. First write the given fact. Then write the pair of sides with its reason. Then press Check.

Try it yourself

$Write the proof$

Write the proof

All lessons in Congruence & Proof

2Congruent Triangles

Same Size, Same ShapeWhat Congruence GivesRecap: Matching Parts

5ASA and AAS

The Side Between The ASA Rule The AAS Rule ASA or AAS?Recap: ASA and AAS

8Proofs with Vertical Angles

Vertical Angles in Proofs The Bowtie Bowtie with ASA Linear Pairs in Proofs Recap: Vertical Angles

11Similarity Proofs