We can classify triangles based on two key features. We can classify them based on their angle measures, as either acute, obtuse, or right, and we can classify them based on their side lengths, as either scalene, isosceles, or equilateral. Every triangle falls under one angle measure type, and one side length type. Let’s look at how we determine each of those classifications. If we’re determining the triangle type based on angle measure, begin by identifying the largest angle measure in the triangle. If that angle is acute, that is to say less than 90 degrees, then the triangle is acute. If the angle is obtuse, meaning greater than 90 degrees, then the triangle is an obtuse triangle. And if the largest angle in the triangle is a right angle, meaning it has a measure of 90 degrees, then the triangle is a right triangle.

So what about the triangle types based on side lengths? For this classification, begin by looking at the three side lengths. If all 3 sides have different lengths, then the triangle is scalene. If exactly two of the side lengths are the same, the triangle is isosceles. And if all three sides have the same length, then the triangle is equilateral, which means equal sides.

So how would we classify this triangle here? Let’s start by classifying based on angle measure. The largest angle in this triangle has a measure of 100 degrees. That is an obtuse angle, so this is an obtuse triangle. Now what about side lengths? This triangle has side lengths of 6, 6, and 9.2. Since exactly 2 of those side lengths are the same, 6 and 6, this triangle is isosceles. So this is an example of an obtuse isosceles triangle.

What about this triangle? Well, the largest angle in this triangle is the right angle, which has a measure of 90 degrees. So by angle measure, this is a right triangle. What about by side lengths. Well, the sides of this triangle have lengths of 8.7, 10, and 5. Since none of those are equal to each other, this triangle is scalene. So this type of this triangle is a right scalene triangle.

Alright, let’s head over to the whiteboard to look at a few more examples.

The instructions read, “Classify each triangle with the given side lengths and angle measurements.” So for our first triangle, it has side lengths of 3.8, 3.8, and 6, and because exactly two of these sides have the same length, then this is an isosceles triangle. Now let's classify it based on angle measurement. Our angle measures are 38 degrees, 38 degrees, and 104 degrees. So our largest angle measure is 104 degrees, which is an obtuse angle, so this is an obtuse triangle. So this triangle is an isosceles obtuse triangle, or an obtuse isosceles triangle. Alright, let's look at the next one.

Our second triangle has side lengths of 13.8, 13.2, and 7. Well none of these three side lengths are equal, so by side length, this is a scalene triangle. Now how do we classify it based on angle measure? Well, our angle measures are 30, 70, and 80. So our largest angle is 80 degrees, which is an acute angle, so this is a scalene acute triangle.

Let's look our third triangle, which has side lengths of 3, 3, and 3, and angle measurements of 60, 60, and 60. Because our three side lengths are all equal to each other, they all have a length of 3, this is an equilateral triangle. Now all equilateral triangles are acute, but we can still put that this is an equilateral acute triangle.

Alright, now let's look at our last triangle, triangle four. It has side lengths of 6, 8, and 10, and angle measurements of 90, 36.9, and 53.1. So first, let's look at the side lengths. These are all three different side length measures, so this is a scalene triangle. Now how do we classify it based on angle measure? Well, the largest angle has a measure of 90 degrees, so this is a scalene right triangle.