CPCTC Proof Practice

This video contains two practice proofs on using CP CTC. Remember that that stands for corresponding parts of congruent triangles are congruent. So if you'd like to hit pause right now and see if you can come up with the four reasons that match the statements given, be a good idea and then come back and check your work with mine. All right, let's see how you did. You are given that BO segment BO and COR congruent. So we'll mark that on our picture. And segment AO and DO are congruent. So we'll mark that. And the reason that those are congruent is that it's given information. Next, we see angle AOB is congruent to angle DOC. Those two angles are congruent by the vertical angle theorem. Or we can just write vertical angles. Our congruent. Now they say the two triangles are congruent. We know four ways of proving triangles congruent right now. And the four ways our side side side, side angle side, angle side angle, and angle angle side. And when I look at the picture, I can evaluate and figure out that it's side angle side. There's a side and a side, another pair of sides, and the angles in between. Once I know the two triangles are congruent, why would it be okay for me to say this angle B and this angle C are congruent? Their corresponding parts. Of congruent triangles, therefore they're congruent. CPC TC. Here's a second proof. Why don't you hit pause, see if you can come up with a 5 reasons, and then play the video again. In this one, we're given SR is congruent to UT. We're given SR is parallel to UT and parallel. We make the arrows. And we know angle S is congruent to angle U so our first reason here is given. And now we'll go back and look and see if we can figure out if this line is parallel to this line, and here's a transversal. Y is angle one, congruent to angle four. They are corresponding angles. So if the lines are parallel, then the corresponding angles are congruent. And when I look at the two triangles, I have an angle pair at the top here and angle pair at the bottom and the side in between. So why are the two triangles congruent? Angle, side angle. After I know the two triangles are congruent, what would give me the right to say angle three and angle two are congruent. We're going to use corresponding parts of congruent triangles or congruent. We're going to use that again. And now I'm supposed to figure out Y is line ST, which is this green line here. Parallel to line or to segment UV, which is this one here. I know 8 ways of proving lines parallel. And drawing in this transversal, and I'm trying to think, okay, if angle two and angle three are congruent, why would the lines be parallel? Because they're corresponding angles. So this would be the corresponding angles, converse. It would be the converse of the reason in number two. Number two, we were proving the angles congruent, and number 5 are proving the lines are parallel. Hopefully, you did well