CPCTC — Geometry, what it means and where it is taught
Corresponding Parts of Congruent Triangles are Congruent — used after proving congruence.
Taught in Geometry.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Corresponding parts — The pieces that match up: A with D, side AB with side DE, and so on.
- Congruent — Same size and same shape. Written △ ABC ≅ △ DEF.
Practise this idea
4 questions in the course bank use CPCTC, in How to Write a Proof, Triangle Congruence Proofs.
Problem 1
CPCTC may be used
- only after proving two triangles congruent
- at any point in a proof
- to prove triangles congruent
- only in coordinate proofs
Worked answer
only after proving two triangles congruent
It is what congruence gives you.
Using it to prove congruence would be circular.
Problem 2
In a proof you want to show AD ≅ CD. What is usually the step before?
Worked answer
prove the triangles containing them are congruent
Prove △ ABD ≅ △ CBD.
Then CPCTC gives the segments.
Problem 3
After proving △ ABC ≅ △ DEF, what reason lets you write ∠ B ≅ ∠ E?
Worked answer
CPCTC
B pairs with E in the correspondence.
So ∠ B ≅ ∠ E by CPCTC.
Problem 4
From △ ABD ≅ △ CBD, which side corresponds to AD?
Worked answer
CD
AD pairs with CD.
AD ≅ CD by CPCTC.