A triangle is a polygon. It is a closed 3-sided shape made up of straight lines.

The ‘tri-’ part of the word triangle means three. A triangle has 3 sides and 3 angles.

Interior angles are the angles that are created inside a shape where the sides meet.

The ​interior angles in a triangle always add up to 180º.

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Types of triangle

A triangle is a 2D shape with three sides.

When you look at triangles carefully you can see that they have similarities and differences.

Take a look at this triangle.

You can see that all three sides have an equal length of 4cm. ​

​The marks on the sides show you that the sides are equal in length.

You could also describe the sides as congruent – they are exactly the same length.

This means that this triangle is equilateral.

Let's look at another triangle.

You can see that there are two sides which have an equal length of 7cm.

This means that this triangle is isosceles. An isosceles triangle has two sides that are ​congruent (equal) in length.

Even if the measurements were not labelled, you would still know it is an isosceles triangle. The tick marks confirm that two of the sides are equal in length.

Here is another triangle.

This time you can see that there are no sides with equal lengths.

This means that this triangle is scalene. A scalene triangle has no sides that are congruent.

Again, if the measurements were not labelled, you would still know it is a scalene triangle because there are not any tick marks on the diagram.

Classifying triangles by the size of their angles

You can also classify a triangle by looking at the size of its angles.

Let’s look at the same triangles but this time focus on the size of the angles.

You can see that there are three equal angles, each measuring 60º.

This means that this triangle is equilateral.

You can also describe the angles as congruent – they are exactly the same size.

This triangle has 2 equal angles, each measuring 75º.

An isosceles triangle has two angles that are congruent.

This means that this triangle is isosceles.

You can see that there are no equal angles in this triangle.

This means that this triangle is scalene.

A scalene triangle does not have any angles that are congruent.

Classifying triangles by sides and angles

Sometimes you need to classify a triangle by looking at the length of the sides and the size of its angles.

This triangle has some information about the length of its sides and some information about its angles.

You can combine this knowledge to classify the triangle.

You can see one angle labelled 40º.

This means the triangle cannot be equilateral, because each angle would need to be 60º.

You can see that two of the sides are equal. You know this because two of the sides have been labelled with a tick to show they are congruent.

This information tells you that this is an isosceles triangle.

Let's look at one more triangle.

You can also use facts you know about other angles to classify triangles.

This triangle has a right angle. We call this a right-angled triangle.

It cannot be an equilateral triangle because that would have 60º angles for all three angles, so none could be 90º.

All right-angled triangles are either isosceles or scalene.

If you look closely, you can see the measurements of two of the sides are not equal.

You can see the vertical side is much shorter than the other two sides, so that means that all the sides are different lengths.

Therefore, this is also a scalene triangle.

Remember, not every right-angled triangle is scalene; an isosceles triangle can also have a right angle.

Example 2

Example 3