 All right, next example. We're given that G, O, and L, F are parallel. O, L, and G are parallel. And our job is to prove that G and L are congruent angles. So the step kind of before proving this is true is we'll want to prove that the two triangles are congruent. So we're going to start by proving the triangles are congruent, and then we can use the CPCTC, like we've seen before, to prove that angle G and angle L are congruent. So first off, let's kind of figure out what we have here. These segments are parallel, G, O, and L, F, and that refers to G, O, and L, F. Well, what of it? Well, with parallel lines, you should always be thinking about angles. And in particular, well, which pair of angles? Those yellow lines are parallel, and they are cut by this transversal, O, F. So if we've got parallel lines here cut by a transversal, we're thinking about angles. And in particular, the only angles that touch those yellow lines are angles 1 and 4. So G, O, parallel to L, F, that gives us angle 1 congruent to angle 4. Next piece of given information is that O, L is parallel to G, F. O, L refers to this segment. And G, F refers to this segment. And they're still cut by that red transversal. However, the angles that are congruent because of that fact are different. Angle 2 is created by a green line. Angle 3 is created by a green line. And so that means that angles 2 and 3 are congruent because O, L is parallel to G, F. So we've got two pairs of angles. The way that this particular image is drawn, we've got a shared segment, O, L. And since we have two pairs of angles, we can either use AAS or ASA. ASA. But which one is right for us? Well, we've got to think about the included side. If you just consider triangle G, O, F, I'll just recreate it down here, G, O, F. So that's this triangle in here, that triangle. So if we just look at that triangle, that triangle, we've got angle 1 up top here. We've got angle 3 down below here. And then we have that shared segment right in the middle. And so this follows angle side, included side angle. So we must use the ASA theorem and can't use AAS. So let's get to it. Let's write the proof. All right, so earlier we talked about using the two triangles congruent as a sub-step along the way. So we want to use the fact that G, O, F, and L, F, O are congruent first. And however, the proof itself, remember, asked us to prove that angles G and L are congruent. And so once we've established that the two triangles themselves are congruent, we can use the CPCTC to say that angles G and L are congruent. So now let's get back to the bulk of the proof up above. We need to talk about a pair of angles, a pair of sides, and another pair of angles. From the given information, we know G, O, G, O, and L, F are parallel, which meant angles 1 and 4 were congruent. Similarly, because O, L is parallel to G, F, angles 2 and angle 3 are congruent. And then lastly, O, F is a shared segment in both triangles. And as a result, it'd be congruent in both G, O, F, and L, F, O. So now our proof is done. Scroll through it so you can take a look at the final proof. It kind of looks like a 6, doesn't it, to be a G.