Triangles

Types of triangle

A triangle is a 2D shape with three sides. There are four different triangles with different properties.

Scalene, Isosceles, Equilateral and right-handed triangles

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 line segments, and they meet at point A. AB joins the points A and B.

The angle between AB and AC is labelled BAC.

Angle BAC

The angle can 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.

Triangle producing unknown angles, g and h, along a line

g is the interior angle. h is the exterior angle. g + h = 180^\circ

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

The sum of interior angles in a triangle

curriculum-key-fact
The sum of interior angles in a triangle is 180°.

To prove a + b + c = 180^\circ, firstly draw a line parallel to one side of the triangle.

Interior angles of a triangle labelled a, b and c

d = b (alternate angles are equal)

e = c (alternate angles are equal)

a + d + e = 180^\circ (angles on a straight line add up to 180°)

So a + b + c = 180^\circ.

These facts can be used to calculate angles.

Question

Calculate the angles m and n.

Triangle on a line, producing unknown angles, m & n

m = 180^\circ - 90^\circ - 50^\circ = 40^\circ

n = 180^\circ - 50^\circ = 130^\circ