# 9.8: Triangle Classification by Side Lengths

**At Grade**Created by: CK-12

**Practice**Triangle Classification by Side Lengths

Remember Cassie from the last Concept?

In that Concept, Cassie learned how to identify triangles according to angle measures. In this Concept, she is going to learn to identify the same triangles according to side length. Take a look.

Here are the triangles that Cassie is going to identify according to side length.

**This Concept will teach you how to classify triangles in this way. By the end of the Concept, you will know how to help Cassie.**

### Guidance

You just learned how to look inside the triangle at its angles to help classify a triangle. Well, we can also look at the lengths of the sides to help us classify triangles.

**No they aren’t the same. Let’s look at how we can classify triangles according to side length.**

**The first triangle to think about is an** *equilateral triangle***. An equilateral triangle has side lengths that are the same. Let’s look at an example.**

**These little lines let you know that the side lengths are the same. Sometimes you will see these and sometimes you won’t. You may have to figure it out on your own or by measuring with a ruler.**

**The second type of triangle is a** *scalene triangle***. A scalene triangle is a triangle where the lengths of all three sides are different. Here is an example of a scalene triangle.**

Here you can see that all three sides of the triangle are different lengths. This is called a scalene triangle.

**The third type of triangle is an** *isosceles triangle***. An isosceles triangle has two side lengths that are the same and one side length that is different. Here is an example of an isosceles triangle.**

Classify these three triangles on your own. Classify them according to their side lengths.

#### Example A

**Solution: Scalene triangle**

#### Example B

**Solution: Equilateral triangle**

#### Example C

**Solution: Isosceles triangle**

Remember Cassie? Here is the original problem once again.

Cassie learned how to identify triangles according to angle measures. In this Concept, she is going to learn to identify the same triangles according to side length. Take a look.

Here are the triangles that Cassie is going to identify according to side length.

Triangles 1, 2, and 4 all have three different side lengths. These are all scalene triangles.

Triangle 3 is an isosceles triangle because two of the side lengths are the same.

### Vocabulary

Here are the vocabulary words in this Concept.

- Triangle
- a three sided figure with three angles. The prefix “tri”means three.

- Scalene Triangle
- all three side lengths are different

- Isosceles Triangle
- two side lengths are the same and one is different

- Equilateral Triangle
- all three side lengths are the same

### Guided Practice

Here is one for you to try on your own.

Can this triangle be an isosceles triangle?

Side lengths, 6 cm, 4 cm, 6 cm

Angles 70, 70, 40 degrees

**Answer**

The angle measures given are helpful, but the side lengths are all that you need to determine whether or not this triangle can be an isosceles triangle. Given that two of the side lengths are the same, it is indeed an isosceles triangle.

### Video Review

Here is a video for review.

James Sousa, Angle Relationships and Types of Triangles

### Practice

Directions: Answer the following questions using what you have learned about triangles their angles and side lengths.

1. If a triangle is a right triangle, then how many angles are acute?

2. How many angles in a right triangle are right angles?

3. How many degrees are there in a right triangle?

4. What is an obtuse angle?

5. How many obtuse angles are in an obtuse triangle?

6. If there is one obtuse angle, how many angles are acute?

7. If a triangle is equiangular, what is the measure of all three angles?

8. What does the word “interior angle” mean?

9. True or false. The side lengths of a scalene triangle are all equal.

10. True or false. The side lengths of a scalene triangle are all different.

11. True or false. The side lengths of an equilateral triangle are all equal.

17. True or false. An isosceles triangle has two side lengths the same and one different.

18. True or false. A scalene triangle can also be an isosceles triangle.

Isosceles Triangle

An isosceles triangle is a triangle in which exactly two sides are the same length.Scalene Triangle

A scalene triangle is a triangle in which all three sides are different lengths.Triangle

A triangle is a polygon with three sides and three angles.### Image Attributions

Here you'll learn to classify triangles by their side lengths.

## Concept Nodes:

Isosceles Triangle

An isosceles triangle is a triangle in which exactly two sides are the same length.Scalene Triangle

A scalene triangle is a triangle in which all three sides are different lengths.Triangle

A triangle is a polygon with three sides and three angles.