ôô What's the difference between equilateral, isosceles, and scalene triangles? How about obtuse, right, and little acute ones? Keep on reading to find out!

By
Jason Marshall, PhD
Episode #215 Triangles are everywhere in the world around us—bridges, rooftops, billiard ball racks, even down at the molecular level, we are surrounded by triangles.

If you've been paying even the slightest bit of attention to those triangles, you know that they come in all sorts of shapes and sizes. Which might lead you to wonder how exactly we go about classifying and describing the shapes of these objects in the triangular zoo?

Wonder no more because that's exactly the question we'll answer today as we learn all about triangles.

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## What Is a Triangle?

Before we learn about how the various types of triangles are classified, let's take a minute to establish exactly what we mean by "triangle." Fortunately, the meaning is right there in the word: "tri" or three and "angle" or, well, angle—three angles. Which is, of course, exactly the number of angles that each and every one of the triangles you know and love have. Obviously no big surprise.

By angles, we're really talking about the points—aka, the vertices—where two lines come together. In order to have three vertices which form those three angles, you've gotta have a three sided shape. And voilà…a triangle.

There are lots of other fun facts to know about triangles—such as the fact that the sum of the angles of each and every triangle in existence must always equal 1800. Why? We'll find out in a future episode—but we'll leave it at that for now and get on to figuring out how we can describe the various types of triangles that we encounter.

## Equilateral, Isosceles, and Scalene Triangles

If you think about it (and perhaps draw a few pictures), you'll see that since a triangle has three sides, it must also have three possible relationships between the lengths of its sides:

1. In an equilateral triangle, all three sides have the same length. Not only are the three legs of an equilateral triangle the same length, but its angles must also all be equal, too (600 apiece if you're counting). If you're having a hard time seeing why this must be so, draw an equilateral triangle and then imagine squishing it one way or another. Can you see that no matter how you squish it the resulting triangle will no longer have equal angles? Only an equilateral triangle can have three equal angles.

2. In an isosceles triangle, two of the three sides (but not all three) have the same length. This word comes from a Greek word meaning something like "equal leg." Given that an isosceles triangle has two equally sized sides, this "equal leg" description makes sense. How many of an isosceles triangle's three angles must be equal? I'll let you think about that, but here's a hint: It's more than none but less than all three.

3. Finally, a scalene triangle is any triangle whose sides all have different lengths. Most triangles are actually scalene, which is probably why most of us don't remember this word. We tend to remember the meaning of equilateral and isosceles because those are special cases, but scalenes are just your ordinary everyday oddballs. How many of a scalene triangle's angles are equal? Think about it…

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