Tasha goes sailing with her father on her father's old boat. The sail looks like a triangle. All of the sides of the sail are different lengths. Tasha wants to classify the triangle but she isn't sure how to name it. Given the side lengths of the triangle, how can Tasha classify the triangle?

In this concept, you will learn how to classify triangles by their side lengths.

### Classifying Triangles by Side Lengths

You can use the lengths of the sides to help you classify triangles.

Let’s look at how to classify triangles according to side length.

An **equilateral triangle** has side lengths that are the same. Here is 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.

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

You can see that all three sides of the triangle are different lengths.

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.

### Examples

#### Example 1

Earlier, you were given a problem about Tasha and her sail.

Her sail is shaped like a triangle with different side lengths. What classification should Tasha give the triangle?

First, determine if any of the side lengths are the same.

No

Then, classify the triangle.

Scalene

The answer is a scalene triangle.

#### Example 2

Classify this triangle as scalene, isosceles or equilateral according to its side lengths.

Side lengths, 6 cm, 4 cm, 6 cm

Angles 70, 70, 40 degrees

First, determine if any of the side lengths are the same.

Yes

Next, determine how many side lengths are the same.

Two

Then, classify the triangle.

Isosceles

The answer is an isosceles triangle.

#### Example 3

Classify this triangle according to its side lengths.

First, determine if any of the side lengths are the same.

No,

Then, classify the triangle.

Scalene

The answer is a scalene triangle.

#### Example 4

Classify the triangle according to its side lengths.

First, determine if any of the side lengths are the same.

Yes

Next, determine how many side lengths are the same.

All of the side lengths are the same

Then, classify the triangle.

Equilateral

The answer is an equilateral triangle.

#### Example 5

Classify the triangle according to its side lengths.

First, determine if any of the side lengths are the same.

Yes

Next, determine how many side lengths are the same.

Two

Then, classify the triangle.

Isosceles

The answer is an isosceles triangle.

### Review

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

- If a triangle is a right triangle, then how many angles are acute?
- How many angles in a right triangle are right angles?
- How many degrees are there in a right triangle?
- What is an obtuse angle?
- How many obtuse angles are in an obtuse triangle?
- If there is one obtuse angle, how many angles are acute?
- If a triangle is equiangular, what is the measure of all three angles?
- What does the word “interior angle” mean?
- True or false. The side lengths of a scalene triangle are all equal.
- True or false. The side lengths of a scalene triangle are all different.
- True or false. The side lengths of an equilateral triangle are all equal.
- True or false. An isosceles triangle has two side lengths the same and one different.
- True or false. A scalene triangle can also be an isosceles triangle.
- True or false. An equilateral triangle is also equiangular.
- True or false. A scalene triangle can not be an acute triangle.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 9.8.