# Classifying Triangles by Angles

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Classifying Triangles by Angles
CCSS.MATH.CONTENT.4.G.A.2

## Measuring Angles in Triangles

In geometry, an angle is formed if two lines or rays meet at a shared point. The two lines are called the sides of an angle and the end point is called the vertex of an angle. They are measured in degrees, which are represented by the symbol °.

There are three important types of angles:

1. Acute angles, an angle less than 90°.
2. Right angles – angles of exactly 90°.
3. Obtuse angles between 90° and 180°.

## What is a Triangle?

A triangle in mathematics is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. All triangles have at least two angles less than 90°.

## Classifying Triangles by Angles

In geometry we can classify triangles based on their angles. Now let’s look at the three different types of triangles below and recognize how different one is from the other.

An equilateral or equiangular triangle has three angles spanning 60º and three sides of the same length.

A right-angled triangle or right triangle has one right angle (90º).

An obtuse triangle is a triangle where one angle is greater than 90º.

## Different Types of Triangles – Summary

Today we have learned about different types of triangles. Let’s summarize what we learned about triangles below:

Type of triangle Description
acute triangle A triangle with two angles measuring less than 90°.
equilateral /
equiangular triangle
A triangle where all three sides are of equal
length and all three angles the same (60º)
.
right angled triangle A triangle with one right angle (90º)
obtuse triangle A triangle with an angle greater than 90°.

To test your knowledge on different types of triangles, have a look at our videos, interactive exercises and printable worksheets.

## Frequently Asked Questions on Different Types of Triangles

What is an angle?
What are the different types of acute triangles?

### TranscriptClassifying Triangles by Angles

Nico and Nia are part of the space clean-up program. They are in charge of the floating triangle debris, and must recycle them based on their angles! Let's join in and learn all about classifying triangles by angles. Today, we will be learning how to classify triangles based on their angles. An angle is the space between two intersecting lines, shown by an arc like this! To sort triangles by their angles, it is important to know that all triangles have at least two angles that are less than ninety degrees, or acute angles. Once you identify the two acute angles, then you can look at the third angle. If the third angle is also less than ninety degrees, the triangle is an acute triangle. There is also a special type of acute triangle called an equiangular triangle where all the angles are sixty degrees. Equiangular means all angles are equal. With this type of triangle, if the third angle is exactly ninety degrees, the triangle is a right triangle. And with this type of triangle, if the third angle is greater than ninety degrees, the triangle is an obtuse triangle. It looks like we are ready to help Nico and Nia with the space cleanup! Here is the first triangle, let's classify it! First, let's identify the two acute angles. Now, let's look at the third angle. What type of triangle is this based on the third angle? It is a right triangle, because the third angle is a right angle. This one can go in the right triangle recycling container! Here is the next triangle, let's classify it! First, let's identify the acute angles. Wait, it looks like ALL the angles are acute angles. What does this mean? If all the angles of a triangle are acute angles, then it's an acute triangle. This one can go in the acute triangle recycling container! Let's help with the final triangle. Which two angles are the acute angles? These two angles are acute angles since they're less than ninety degrees. Based on the third angle, what type of triangle is this? The third angle is an obtuse angle, so it is an obtuse triangle. This one can go in the obtuse triangle recycling container. While Nico and Nia finish up their day, let's review. Remember, triangles can be classified based on their angles. First, identify the two acute angles. Then, look at the third angle. If the third angle is less than ninety degrees, it is an acute triangle. If the third angle is exactly ninety degrees, it is a right triangle. If the third angle is greater than ninety degrees, it is an obtuse triangle. "You know, I did see a cute triangle out there!" "That's not right, Nico. Don't be so obtuse!"

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1. I LOVE THIS!!!!!!!#1

From MOJOLA , about 1 year ago

## Classifying Triangles by Angles exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Classifying Triangles by Angles.
• ### What type of angle is it?

Hints

Remember:

• Acute angles are less than 90°
• Right angles are exactly 90°
• Obtuse angles are greater than 90°

This is a picture of a right angle. Right angles look like corners.

If an angle is smaller than a right angle, it is an acute angle.

If an angle is greater than a right angle, it is an obtuse angle.

Nico has measured the angles. Look at each angle. Is it less than 90°, exactly 90°, or greater than 90°?

Solution

The image above shows each angle's classification.

You can find out whether an angle is acute, right, or obtuse, by thinking about how many degrees are in the angle.

• acute angles are less than 90°
• right angles equal 90°
• obtuse angles are more than 90°

• ### What is the correct description?

Hints

Look at the name of each triangle type, this gives you a clue as to what types of angles the triangle has.

For example, an obtuse triangle has one obtuse angle.

In an equiangular triangle, all of the angles have the same number of degrees.

Solution

Above are the types of triangles and their descriptions.

All triangles have two acute angles. You can figure out the type of triangle by thinking about the third angle.

• ### Can you classify the triangles by their angles?

Hints

Look at the name of each triangle type, this gives you a clue as to what types of angles the triangle has.

For example, in an equiangular triangle, all angles are equal.

Which picture shows a triangle that has three angles that are equal?

Every triangle has two acute angles. Find the two acute angles, then look at the third angle to figure out what type of triangle it is.

Is the third angle less than, equal to, or more than 90°?

Solution

The answers are shown in the image above.

• Right triangles have one 90° angle.
• Acute triangles have three angles less than 90°.
• Obtuse triangles have one angle greater than 90°.
• Equiangular triangles have three equal, 60° angles.
• ### What type of triangle is it?

Hints

All triangles have two acute angles. Identify the two acute angles, then look at the third angle.

Is the third angle less than, equal to, or more than 90°?

Look at the name of each triangle type, this gives you a clue as to what types of angles the triangle has.

For example, in an acute triangle, all angles are acute.

Solution

Above is an image with the correct answers.

• Right triangles have one 90° angle.
• Acute triangles have three angles less than 90°.
• Obtuse triangles have one angle greater than 90°.
• ### Can you classify the triangle?

Hints

Every triangle has two acute angles.

Find the two acute angles, then look at the third angle to figure out what type it is.

Is the third angle less than, equal to, or more than 90°?

• If the third angle is less than 90°, it is an acute triangle.
• If the third angle is equal to 90°, it is a right triangle.
• If the third angle is more than 90°, it is an obtuse triangle.
Solution

This triangle is a right triangle because it has one 90° angle.

• ### How do you describe the different types of triangles?

Hints

Acute triangles have the most acute angles out of all the types of triangles.

Right angle is another name for a 90° angle.

Solution

Here are the correct sentences:

• All triangles have at least two angles that are acute angles.
• Acute triangles have three acute angles.
• Right triangles have one angle that is exactly 90°.
• Obtuse triangles have one angle that is greater than 90°.