 Chapter 4 deals with triangles. In particular, it deals with relationships between two triangles. So when we talk about congruent triangles, what do we mean? Triangles that are congruent have the exact same sides and the exact same angles as each other. And we'll get into an example in just a second. So we have this very important acronym. We call it corresponding parts of congruent triangles are congruent. So let's break this down a little bit. We've got parts of triangles. So we're talking about two separate triangles. Let's give you an example here. So let's say we have these two triangles, triangle NBC and triangle FOX. If we know that these two triangles are congruent, then all the parts are congruent as well. So for example, side length NB is congruent to side length FO. BC is congruent to OX. NC is congruent to FX. So all the sides are congruent. Also, the angles are all congruent. So for example, angle N has to be congruent to angle F. Angle B has to be congruent to angle O. And angle X and angle C are also congruent. So that's what we mean when we talk about corresponding parts. Corresponding basically means parts that are in the same spot. So if I talk about angle N, I see angle N and angle F are both kind of in the first position of the names. So that means angle N and angle F have to be corresponding congruent parts. So that's the CPCTC. CPCTC, you can say it really fast if you want to. Corresponding parts of congruent triangles are congruent. So it just so happens that the CPCTC is a biconditional. So if we have congruent triangles, then corresponding parts are congruent. Likewise, if corresponding parts are congruent, then the triangles themselves are congruent. So that's going to be a helpful tool when we use this statement to prove triangles are congruent or prove certain parts of triangles are congruent. So the CPCTC, it's a helpful thing. Make sure it's in your notes. Here's a brief example. Let's say we know that triangle ABC is congruent to triangle XYZ. Well, XYZ is over here. It's not labeled. So we'll have to go and label it. I see angle A. A is kind of in the corner here, this right angle looking like corner. And since A comes first in the name ABC and X also comes first, that means X is the corresponding angle to angle A. Likewise, Y and B are corresponding because I see B and Y sort of share the same space. Now B, I see B is kind of attached to this short leg and this long hypotenuse. So that means angle Y also has to be attached to the short leg and the long hypotenuse. So there's angle Y. And then lastly C is kind of at the pointy end of this triangle. So that means Z for the corresponding side has to also be in that pointy side. So according to the CPCTC, we know a ton of different things are congruent. All of the angles are congruent. So we can go through and start labeling. I know angle A must be congruent to angle A follows X. So angle X. So we know all three pairs of these corresponding angles are congruent. Angle A is congruent to angle X. B is corresponding and congruent to angle Y. And Z and C are congruent as well. So that deals with the angles. Also the sides are congruent. A, C congruent to X, Z. So that means this side length is congruent to that side length. Hypotenuse is congruent to the other hypotenuse and that long leg is congruent to that long leg. One last example here. Let's pretend like we have triangle CAT and we know it's congruent to triangle DOG. Without drawing any pictures of triangles, we can figure out the completions of these sentences. Segment TA. TA refers to those two sides. TA would be congruent to segment GO. Because it follows the same order in the name. T to A, G to O. Angle C. Angle C is that first angle and it corresponds with the first angle in DOG. So angle C is congruent to angle D. And then finally segment DG. Well DG is like first, last in the name DOG. So first and last, first and last. So segment CT would be the segment that's congruent to segment DG.