Home

Maths

Shapes

Triangles and regular polygons: Types and properties

Triangles and regular polygons: Types and properties

Select Lesson

Proportion


Ratio


Explainer Video

Loading...
Tutor: Alice

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°\ {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.
Maths; Shapes; KS3 Year 7; Triangles and regular polygons: Types and properties
Isosceles
  • Two equal sides. 
  • Two equal angles.
Maths; Shapes; KS3 Year 7; Triangles and regular polygons: Types and properties
Scalene
  • No equal sides.
  • No equal angles.
Maths; Shapes; KS3 Year 7; Triangles and regular polygons: Types and properties
Right-angled

  • Contains a right-angle. 
  • Triangles can be isosceles and right-angled.
  • The side opposite the right-angle is the longest side (hypotenuse).
Maths; Shapes; KS3 Year 7; Triangles and regular polygons: Types and properties



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°\ {60 \degree}​​
 3\ {3}​​
Maths; Shapes; KS3 Year 7; Triangles and regular polygons: Types and properties
Square
 90°\ {90 \degree}​​
 4\ {4}​​
Maths; Shapes; KS3 Year 7; Triangles and regular polygons: Types and properties
Pentagon 
 108°\ {108 \degree}​​
 5\ {5}​​
Maths; Shapes; KS3 Year 7; Triangles and regular polygons: Types and properties
Hexagon 
 120°\ {120 \degree}​​
 6\ {6}​​
Maths; Shapes; KS3 Year 7; Triangles and regular polygons: Types and properties
Heptagon
 128.6°\ {128.6 \degree}​​
 7\ {7}​​
Maths; Shapes; KS3 Year 7; Triangles and regular polygons: Types and properties
Octagon 
 135°\ {135 \degree}​​
 8\ {8}​​
Maths; Shapes; KS3 Year 7; Triangles and regular polygons: Types and properties



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.


Create an account to read the summary

Exercises

Create an account to complete the exercises

FAQs - Frequently Asked Questions

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

What are the four types of triangle?

What is a regular polygon?

Beta

I'm Vulpy, your AI study buddy! Let's study together.