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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°\ {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.


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.

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