Triangles and regular polygons: Types and properties

In a nutshell

Triangles can be classified as right-angled, equilateral, isosceles or scalene, depending on their properties. All interior angles in a triangle add up to $\ {180 \degree}$ . A regular polygon is a polygon with equal sides and equal interior angles.

Types of triangles

Triangle	properties	Diagram
Equilateral	Three equal sides. Three equal angles. Regular polygon.
Isosceles	Two equal sides. Two equal angles.
Scalene	No equal sides. No equal angles.
Right-angled	Contains a right-angle. Triangles can be isosceles and right-angled. The side opposite the right-angle is the longest side (hypotenuse).

Regular polygons

A regular polygon is a polygon with equal sides and equal interior angles.

Regular polygon	Interior angles	Number of sides	Diagram
Equilateral triangle	$\ {60 \degree}$	$\ {3}$
Square	$\ {90 \degree}$	$\ {4}$
Pentagon	$\ {108 \degree}$	$\ {5}$
Hexagon	$\ {120 \degree}$	$\ {6}$
Heptagon	$\ {128.6 \degree}$	$\ {7}$
Octagon	$\ {135 \degree}$	$\ {8}$

Example 1

Can you identify the type of triangle based on its properties described below?

One right angle.
Two equal interior angles.
Two equal sides.

First, it can help to sketch the triangle.

Maths; Shapes; KS3 Year 7; Triangles and regular polygons: Types and properties

Based on these properties, the shape is a right-angled isosceles triangle.

Example 2

Is a shape with eight equal sides and eight equal interior angles a regular polygon?

Yes, as all shapes with equal sides and equal interior angles are regular polygons.

This shape is an octagon.