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What is a Scalene Triangle? - Definition, Properties & Examples

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  • 0:00 Definition Of A…
  • 0:45 Properties Of Scalene…
  • 2:30 Examples Of Scalene Triangles
  • 2:55 Importance Of Scalene…
  • 3:50 Lesson Summary
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Lesson Transcript
Instructor: Elizabeth Often

Elizabeth has taught high school math for over 10 years, and has a master's in secondary math education.

Have you ever wondered how we classify triangles? In this lesson, we'll learn the definition of a scalene triangle, understand its properties, and look at some examples.

Definition of a Scalene Triangle

You have probably seen many triangles in your life. Perhaps you've even noticed that there are many different types of triangles. Some of these triangles have all three sides of the same length, some have two sides of the same length, and in some triangles, all three sides are different lengths.

Scalene triangles are triangles with three sides of different lengths. The math term for sides of different triangles is noncongruent sides, so you may also see this phrase in your math book. For example, a triangle with side lengths of 2 cm, 3 cm, and 4 cm would be a scalene triangle. A triangle with side lengths of 2 cm, 2 cm, and 3 cm would not be scalene, since two of the sides have the same length.

The hash marks on each side of the scalene triangles show that all sides are different lengths.
TwoScaleneTriangles

Properties of Scalene Triangles

The most important property of scalene triangles is that they have three sides of different lengths. However, they have some other important properties, too. Like other triangles, all the angles inside a scalene triangle add up to 180 degrees. And just like all the sides of a scalene triangle have different lengths, all the angles of a scalene triangle have different measures.

Let's take a look at some examples of triangles that we can classify as scalene or not scalene by their angle measures:

  • 40 degrees - 50 degrees - 90 degrees is a scalene triangle since all the angle measures are different.
  • 60 degrees - 60 degrees - 60 degrees is not a scalene triangle since the angle measures are not all different.
  • 120 degrees - 10 degrees - 50 degrees is a scalene triangle since all the angle measures are different.

The triangle on the left is scalene because it has three different angles. The triangle on the right is NOT scalene because it has two angles of the same size.

Scalene And Not Scalene

In addition, there are some other properties that you might find useful as you encounter scalene triangles in math problems.

  • The longest side of the triangle is opposite the largest angle. This means that in the 120-10-50 triangle above, the longest side of the triangle is across from the 120-degree angle.
  • The shortest side of the triangle is opposite the smallest angle. This means that in the 120-10-50 triangle, the shortest side is located across from the 10-degree angle.

This picture shows these concepts more clearly. In the picture, the bright green side, labeled longest side, is across from the largest angle, B. The shortest side, in black, is across from the smallest angle, angle C.

In the picture, the longest side is across from the largest angle. The shortest side is across from the smallest angle.
LongestShortestSide

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