Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
CPCTC is an acronym for corresponding parts of congruent triangles are congruent. CPCTC is commonly used at or near the end of a proof which asks the student to show that two angles or two sides are congruent. It means that once two triangles are proven to be congruent, then the three pairs of sides that correspond must be congruent and the three pairs of angles that correspond must be congruent.
If you accept the fact that two triangles are congruent, then you must also accept the fact that CPCTC must also apply too. But what is CPCTC besides the Geometry teacher's way of if you're chewing gum. Well it's stands for Corresponding Parts so that the CP of Congruent Triangles, I'm highlighting the letters here are Congruent, so what that means is that if you have two things that are the same every part of those two parts must also be the same as well.
Let's look at a quick example to apply CPCTC. So let's say we had two triangles what I said these two triangles are congruent. I'm going to ask you what are 3 pairs of corresponding congruent parts? Corresponding means they're in the same position in the 2 triangles. Congruent because we accept the fact that these two must be congruent so let's pick out an angle c if I look at angle c, the congruent corresponding part must be angle f and how did I know that? Well there's two ways, one I can look at a and b and say a has 1 mark b has 2 marks d is 1 mark e has 2 marks so the only angle in this triangle that doesn't have a congruence mark is f. I could also look at this order right here that order is very specific. It says if angle c in this triangle is congruent to something in another triangle, it has to be angle f because c is the third letter and f is the third letter it has for two more pairs.
Let's talk about this side bc, so I'm going to say line segment bc is congruent to its corresponding segment in the other triangle which is ef. And last we could look at this line segment ac, its corresponding line segment in the another triangle. If I just look at these letters a is the first letter c is the last letter, so looking at this one d is the first f is the last. I can also look at the drawing to verify that's true when do we use CPCTC? Most often in proofs so if you want to take a look at how to apply it check out the episode on proofs.