 In this video we're going to talk about classifying triangles, using the angle sum theorem for triangles, and also the exterior angle theorem for triangles. But first we're going to talk about classifying triangles. So that word classify, what does it mean? Well, what it means is we're going to try and organize possible types of triangles, and we're going to organize them by their sides and by their angles. So let's begin. So if we talk about classifying triangles by their angles, there are three ways to do that. An obtuse triangle is one in which one of the angles is obtuse. In other words, it's greater than 90, but less than 180. A right triangle is similar. A right triangle has one right angle. And then lastly, an acute triangle has not one, but has all of its angles or acute angles. So we have a special name for an acute triangle when all of the three angles are also congruent to each other. If all three of those angles are congruent, then we have what's called an equi-angular triangle. Next, we're going to talk about classifying triangles by their sides. We have two main types. There's a scalene triangle and an isosceles triangle. In a scalene triangle, none of the sides are congruent. In an isosceles triangle, at least two of the sides are congruent. So since there are three sides in a triangle, if we have all three sides congruent, then we have a special name for that. And now it turns out that these two green statements are related. If we have a triangle that is equi-angular, then I know for a fact that it must be equilateral. Likewise, if we have an equilateral triangle, then that triangle is equi-angular. In other words, we can draw the biconditional statement between the two statements. If we have an equi-angular, then we have equilateral. If we have equilateral, then we have equi-angular. So let's take a little bit of practice with this. Can you classify the top three triangles by their sides? What about the bottom three triangles? Can you classify them by their angles? What about this triangle? Can you classify it fully? In other words, can you classify it both by its sides and also by its angles? Well according to these little congruence marks, none of the sides are congruent. And so that means I have a scalene triangle. And then each of these angles, the red congruence marks, shows that none of the angles are congruent. And furthermore, angle B here looks obtuse to me. And so this triangle is scalene and obtuse. So we classified this triangle in two ways by sides and by angles. What about this one? Pause the video. Try it out yourself. This triangle, C-A-T, is scalene and right. And how about this one? Make sure you recognize these congruence marks. This triangle is isosceles and also obtuse.