Classifying Triangles by Angles and Sides

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  • 0:05 Classifying Triangles
  • 0:45 Scalene, Isosceles &…
  • 2:46 Acute, Obtuse & Right…
  • 4:57 Lesson Summary
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Lesson Transcript
Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Not all triangles are the same. There are equilateral, isosceles and scalene triangles. Then there are right, acute and obtuse triangles. In this lesson, we'll learn how to classify triangles using their sides and angles.

Classifying Triangles

If we want to classify triangles, there's no better expert than Goldilocks. You remember Goldilocks, right? She's the girl who broke into a home owned by some bears, stole some porridge, slept in several beds, and then fled when the bear homeowners returned.

Well, after serving some jail time (bears are rather litigious), Goldilocks gave up her life of crime and is here to help us by using her unique expertise with things that come in threes, like triangles.

Triangles, of course, are two dimensional shapes with three sides and three angles. But like bowls of porridge, not all triangles are the same. Let's let Goldilocks teach us more.

Scalene Triangles

The first way we classify triangles is based on their sides. There are three kinds of these triangles to know.

First, there's this triangle:

Scalene triangle
scalene triangle

Goldilocks doesn't much like this triangle. None of the sides are equal in length. Since there is a direct correlation between the sides and the angles opposite the sides, there also aren't any equal angles. This is like a cold bowl of porridge, all around uneven. It's also a scalene triangle.

A scalene triangle is a triangle with no equal sides or angles. The word 'scalene' actually means uneven or unequal. Imagine uneven scales. As for Goldilocks, she remembers scalene triangles by remembering how gross cold porridge is. If there was a word for that clumpy, icky stuff, it might be scalene.

Isosceles Triangles

Then there's this triangle:

Isosceles triangle
isosceles triangle

Notice those hash marks on two of the sides. That means the sides are congruent. This is an isosceles triangle. An isosceles triangle is a triangle with two equal sides and two equal angles.

Goldilocks likens this one to a hot bowl of porridge. It's not perfect, but it's not bad. With an isosceles triangle, there's nice symmetry.

Plus, if you know one angle, you know them all. In the triangle below, we know one bottom angle is 70 degrees. Since the two sides are congruent, the angles opposite them are also congruent, making the other bottom angle also 70 degrees. And since the sum of the interior angles of a triangle is 180 degrees, the final angle is 40 degrees.

If you know one angle of an isosceles triangle, you can determine the other two.
isosceles triangle

Equilateral Triangle

Then we get to this equilateral triangle:

Equilateral triangle
equilateral triangle

An equilateral triangle is a triangle with three equal sides and three equal angles. Think 'equal' to remember 'equilateral.' Since all the angles must add up to 180 degrees, each angle in an equilateral triangle is just 180 divided by 3, or 60 degrees. This is Goldilocks' favorite triangle. It's like that perfect bowl of porridge. Everything is just right.

Acute Triangles

Scalene, isosceles and equilateral are three classifications of triangles, but there's another way to label these shapes that's solely based on their angles.

Goldilocks thinks of these like those beds she tested at the bears' house. This first one, seen below, is all pointy and uncomfortable. We call it an acute triangle. A triangle is acute if all angles are less than 90 degrees.

In acute triangles, all angles are less than 90 degrees.
acute triangle

Now, you can combine names. Remember our equilateral triangle? That was also acute. And the isosceles triangle we looked at? Also acute.

Obtuse Triangles

Here's the opposite of an acute triangle:

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