Back to Edexcel Angles, Lines & Polygons (F) Home

4.1 A) Triangles

4.1 A) Triangles

In this section, we are going to look at the different types of shapes starting with triangles.

**Triangles**

A triangle is a two-dimensional (2D) shape that has 3 sides, 3 angles and 3 vertices (corners/ intersecting lines). All of the angles in a triangle add up to 180°.

There are four different types of triangle; equilateral, isosceles, right-angle and scalene.

**Equilateral Triangle**

All of the sides on an equilateral triangle are the same length; we indicate that the sides are the same length by placing a small dash on the line. Equilateral triangles also have angles that are of the same size; all of the angles in an equilateral triangle are 60° (180° ÷ 3).

**Isosceles Triangle**

An isosceles triangle has 2 sides that are the same length (the two sides that are the same length have a dashed line through them). Two of the angles in an isosceles triangle are the same size. These are the two angles between the side that is a different length and the two sides that are the same length. For the above triangle, the bottom two angles are the same (the orange angles).

**Right-Angle Triangle**

A right-angle triangle is a triangle that has right-angle in it (a 90° angle). We indicate that an angle is a right angle by placing a small square box in the right-angle angle.

**Scalene Triangle**

All of the sides in a scalene triangle are of different lengths. As the lengths are unequal, so are the angles in the triangle.

**A Few Examples**

We are now going to have a look at a few different triangle examples. The first step in answering the following questions is to first identify what type of triangle we have; is the triangle an equilateral, isosceles, right-angle or scalene? We then use the type of triangle to help us find the size of the unknown angle.

**Example 1**

What is the size of angle

*x*?

The first step in answering this question is to identify what type of triangle we have. The triangle above is an isosceles triangle. We can tell this because 2 of the lengths in the triangle are the same (the two lengths that are the same have a dash through them). This means that the two angles between the length that is not the same and the lengths that are the same will be the same size; on the triangle above, the two angles at the bottom are the same as one another – they are both 70°.

We now have two angles in the triangle and we know that all of the angles in a triangle add up to 180°. Therefore, we can create the following equation from this information:

We can now solve to find the value of

*x*. The first step in finding the value of*x*is to collect the numbers on the left side of the equation.In order to find the value of

*x*, we need to move the 140 from the left side of the equation to the right. We are able to do this by doing the opposite; we take 140 from both sides of the equation.Therefore, angle

*x*is 40°.**Example 2**

What is the size of angle

*y*in the triangle below?

The triangle above is a right-angle triangle and we know this because one of the angles has a small box in it. The angles that has a box in it is 90°. We now have two of the angles in the triangle and we know that all of the angles inside a triangle add up to 180°. Therefore, we can create the following equation:

We now solve to find the value of

*y*. The first step is to collect the two numbers on the left side of the equation.We find the value of

*y*by moving the 130 from the left side of the equation to the right. We are able to do this by taking 130 from both sides of the equation.Angle

*y*in the triangle above is 50°.**Example 3**

What is the size of angle

*z*in the triangle below?

The triangle above is an isosceles triangle because two of the lengths are the same (the sides that are the same length have a dash through them). This means that the two angles between the length that is not the same and the lengths that are the same will be the same size; the two angles on the left of this triangle are the same. The bottom left angle is

*z*and we know that this angle will be the same size as the top left angle. Therefore, we can label the top left angle as*z*as well. The labelled triangle is shown below.We know that all of the angles in a triangle will add up to 180°. Therefore, we can create the following equation:

We can collect the

*z*’s on the left side of the equation.We want to find the value of

*z*. We are able to do this by getting all of the*z*terms to one side of the equation and all of the numbers to the other side of the equation. I am going to get all of the*z*terms to the left side of the equation and all of the numbers to the right side of the equation. This means that I need to move the 110 from the left side of the equation to the right. I am able to do this by doing the opposite; I take 110 from both sides of the equation.We want to find the value of

*z*and not 2*z*. Therefore, we divide both sides of the equation by 2.This tells us that angle

*z*is 35°.