Chapter Overview Maths

Types of numbers

Number calculations

Fractions, decimals and percentages

Algebraic manipulation

Formulae and equations

Straight line graphs

Other graphs

Ratio

Proportion

Rates of change

Shapes

Properties of shapes

Measures

Lines and angles

Drawing shapes

Trigonometry

Probability

Statistics

Maths

# Triangles and regular polygons: Types and properties 0%

Summary

# 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

#### 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.

#### 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.

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.

FAQs

• Question: What shape has three equal sides and three equal interior angles, and what kind of polygon is it?

Answer: A shape with three equal sides and three equal interior angles is an equilateral triangle, which is a regular polygon.

• Question: What are the four types of triangle?

Answer: The four types of triangle are right-angled, equilateral, isosceles and scalene.

• Question: What is a regular polygon?

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

Theory

Exercises