All About Triangles

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

Jason Marshall, PhD
5-minute read
Episode #215

Acute, Obtuse, and Right Triangles

The triangle classification fun doesn't stop there! The terms equilateral, isosceles, and scalene describe the relationships (or lack thereof) between the lengths of a triangle's legs, but they don't say anything about the size of its angles. For that, we have the three additional terms: acute, obtuse, and right.

A small-angled "acute" triangle surely must be "a cute" triangle.

The idea here is pretty simple. An acute triangle is one whose angles are all smaller than 900. You can remember this since a small-angled "acute" triangle surely must be "a cute" triangle. An obtuse triangle, on the other hand, has one angle that's greater than 900. And, as we've encountered many times over the years, a right triangle has one angle that's a right—i.e., 900—angle.

That's all there is to it! With these two classification schemes for describing both the legs and the angles of a triangle, you can pretty well pin down the gist of a triangle's shape—at least well enough to knit it a nice sweater.

Triangles, Rectangles, and Squares

Before we finish up, I'd like to take a minute to talk about last week's episode about the area of triangles. In particular, to address a mistake I made near the end of the show that the eagle-eared among you may have caught.

When talking about how to calculate the area of a triangle, I described how you can imagine taking a right triangle, making an imaginary copy of it, spinning it around 1800, and then nestling the copy up hypotenuse-to-hypotenuse with the original. I then went on to say that the resulting shape is a perfect square. But, as was pointed out by attentive math fans, that's wrong—the resulting shape is a rectangle, not necessarily a square. Of course, it could be a square if the right triangle we started with was isosceles, but it doesn't have to be.

Everything I said after that about how you can use this picture to see where the area formula for a triangle comes from is still perfectly true. You just might not have been looking at a perfect square to see it.

Wrap Up

OK, that's all the math we have time for today.

Please be sure to check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Triangle image courtesy of Shutterstock..


About the Author

Jason Marshall, PhD

Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.