# Triangles

## Types of triangle

A triangle is a shape with three sides. There are four different triangles with different properties.

A scalene triangle has 3 sides of different lengths and 3 unequal angles.

An isosceles triangle has 2 sides of equal length. The dashes on the lines show they are equal in length. The angles at the base of the equal sides are equal.

An equilateral triangle has 3 sides of equal length. The dashes on the lines show they are equal in length. All of the angles are also equal.

A right-angled triangle is a triangle that has a right angle.

## Labelling angles and sides

Letters can be used to label angles.

AB and AC are , and they meet at point A. AB joins the points A and B.

The angle between AB and AC is labelled BAC.

The angle can be written as BAC or BÂC or ∠BAC.

## Interior and exterior angles

The angles inside a shape are called interior angles.

If the side of a triangle is extended, the angle formed outside the triangle is the exterior angle.

is the interior angle. is the exterior angle.

The interior angle and its corresponding exterior angle always add up to 180°.

## The sum of interior angles in a triangle

The sum of interior angles in a triangle is 180°.

To prove , firstly draw a line parallel to one side of the triangle.

(alternate angles are equal)

(alternate angles are equal)

(angles on a straight line add up to 180°)

So .

These facts can be used to calculate angles.

Question

Calculate the angles and .