CPCTC
Related Topics:
More Lessons for Grade 9 Math
Geometry
Examples, solutions, videos, worksheets, and activities to help Geometry students learn about CPCTC.
What is CPCTC?
CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.
What does it mean?
It’s a fundamental theorem used in geometric proofs. It essentially states that if you have proven that two triangles are congruent, then you can conclude that all of their corresponding sides and all of their corresponding angles are also congruent (equal in measure).
The following diagram gives the definition CPCTC (Corresponding Parts of Congruent Triangles are Congruent). Scroll down the page for more examples and solutions on how to use CPCTC.
How is CPCTC used in proofs?
CPCTC is usually the final step in a geometric proof where your goal is to show that two specific segments or angles are congruent.
The typical flow of a proof using CPCTC is:
- Identify two triangles in your diagram that you suspect are congruent.
- Gather evidence (given information, definitions, postulates, theorems like vertical angles, reflexive property, alternate interior angles, etc.) to prove that these two triangles are congruent. You use one of the triangle congruence
postulates/theorems to do this:
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAS (Angle-Angle-Side)
HL (Hypotenuse-Leg, for right triangles only) - State that the two triangles are congruent using the appropriate congruence postulate/theorem. For example, “△ABC≅△DEF by SAS."
- Apply CPCTC: Once you’ve established that the triangles are congruent, you can then use CPCTC to state that any pair of their corresponding parts (sides or angles) are congruent. This is the step that allows you to prove your original goal.
Videos
CPCTC Triangle Congruence
CPCTC Congruent Triangles Geometry Proof
How to use CPCTC in congruent triangle geometry proofs?
SSS, SAS, ASA Proofs with CPCTC
Check out our most popular games!
Fraction Concoction Game:
Master fractions in the lab: mix, add, and subtract beakers to create the perfect concoction!
Fact Family Game:
Complete fact families and master the link between addition & subtraction and multiplication & division.
Number Bond Garden:
Clear the board by matching number pairs that sum to ten in this garden-themed mental math puzzle.
Online Addition Subtraction Game:
Practice your addition and subtraction skills to help the penguin find its mummy.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.