 This shape kind of looks similar to the first proof that we dealt with we've got two triangles and they share a side length However, the given information is different. We've got these segments. Let's call it MA and HT those segments are Parallel right, that's what that little arrow means and Parallel lines always always always give us angles So these parallel lines are cut by a transversal to give us these two angles So those two angles are congruent Now furthermore these segments have these congruence tick marks on them and as a result MA and HT are also congruent So they're both congruent and they're also parallel and then finally we've got a shared side of the middle Segment AT and I know those segments are always congruent to themselves So we can prove that these two triangles are congruent using the side angle side theorem We've got the green side length the red angles and the blue share side shared sides So we're dealing with the side angle side So let's let's piece this together First we know MA is parallel to HT and we also know that MA is congruent to HT All right, so let's talk about those green sides. We know MA and HT are congruent That's given information Next we want to talk about the two red angles that we had we had angle MAT and angle HT But why is that true? Well, that's true because of this given information the two parallel lines So we have to mention that fact. So the fact that MA Is parallel to HT If we have parallel lines then alternate interior angles are congruent So I know it's a bit abbreviated but that reason right the connector with the arrow says if parallel lines Then alternate interior angles are congruent And then finally we have the blue sides We have segment AT and it's a shared segment and shared segments are always congruent Now we're not quite finished with this proof Yeah, we've proven that the two triangles are congruent MAT and HTA But that's not exactly what we're trying to prove We want to prove that angles M and H are congruent in other words We want to prove that these angles are congruent H and M Well in order to do that we're going to use the CPCTC See once we've established that the two triangles are congruent then all of the parts of the two triangles are congruent That's what CPCTC stands for corresponding parts of congruent triangles are also congruent And so we can say given the fact that triangle MAT is congruent to HTA That means angle M must be congruent to angle H and now we're done with the proof