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

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

What are the four types of triangle?

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

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Chapter Overview

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Maths

Triangles and regular polygons: Types and properties

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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.

Triangles and regular polygons: Types and properties

In a nutshell

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.

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.

Frequently Asked Questions (FAQ)

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

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Triangles and regular polygons: Types and properties

Triangles and regular polygons: Types and properties

In a nutshell

Types of triangles

Triangle

properties

Diagram

Regular polygons

Regular polygon

Interior angles

Number of sides

Diagram

Example 1

Example 2

Triangles and regular polygons: Types and properties

In a nutshell

Types of triangles

Triangle

properties

Diagram

Regular polygons

Regular polygon

Interior angles

Number of sides

Diagram

Example 1

Example 2

Theory understood?