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