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Quadrilaterals: Types and properties

Quadrilaterals: Types and properties

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Summary

Quadrilaterals: Types and properties

In a nutshell 

Quadrilaterals are four-sided shapes, with four corners and four sides. Angles in a quadrilateral add up to 360°360\degree​​. There are many different kinds of quadrilaterals. 



Properties of quadrilaterals 

NAME

PROPERTIES

DIAGRAM

Square
  • The only regular quadrilateral.
  • Four sides of equal length.
  • Four right angles.
  • The diagonals bisect at right angles.
  • The diagonals are of equal lengths. 
  • Two pairs of parallel sides.
Maths; Shapes; KS3 Year 7; Quadrilaterals: Types and properties
Rectangle
  • Two pairs of equal sides.
  • Four right angles.
  • Two pairs of parallel sides.
  • The diagonals bisect each other.
Maths; Shapes; KS3 Year 7; Quadrilaterals: Types and properties
Rhombus
  • All four sides are of equal length.
  • Opposite sides are parallel.
  • Opposite angles are equal.
  • The diagonals bisect at right angles.
  • A type of parallelogram.
Maths; Shapes; KS3 Year 7; Quadrilaterals: Types and properties
Parallelogram
  • Opposite sides are the same length.
  • Opposite sides are parallel.
  • Opposite angles are equal.
  • Diagonals bisect. 

Maths; Shapes; KS3 Year 7; Quadrilaterals: Types and properties
Trapezium
  • Only one pair of parallel sides.
Maths; Shapes; KS3 Year 7; Quadrilaterals: Types and properties
Kite
  • Two pairs of equal sides adjacent to each other.
  • One pair of opposite angles are equal.
  • No sides are parallel.
  • Diagonals cross at right angles.
  • One line of symmetry.
Maths; Shapes; KS3 Year 7; Quadrilaterals: Types and properties
Arrowhead
  • Two sets of adjacent sides are equal.
  • One interior angle is a reflex angle. 
  • Two interior angles adjacent to the reflex angle are equal.
  • Contains one line of symmetry. 
Maths; Shapes; KS3 Year 7; Quadrilaterals: Types and properties



Example 1 

Can you identify this quadrilateral from its properties?

Properties include: 

  • It has four sides of an equal length.
  • Opposite sides are parallel.
  • Opposite angles are equal.
  • Its diagonals bisect at right angles.
  • Has no interior right angles. 


First it can help to sketch the shape to identify it.

Maths; Shapes; KS3 Year 7; Quadrilaterals: Types and properties


​Therefore, this quadrilateral is a rhombus.


Example 2 

Can you identify this quadrilateral from its properties?

Properties include:​

  • Two pairs of equal sides adjacent to each other.
  • One pair of opposite angles are equal.
  • No sides are parallel.
  • Diagonals cross at right angles.
  • It has one line of symmetry. 

First it can help to sketch the shape to identify it.​

Maths; Shapes; KS3 Year 7; Quadrilaterals: Types and properties

Therefore, this quadrilateral is a kite.

​

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Exercises

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8 Exercises

Medium

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Hard

5 Exercises

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FAQs - Frequently Asked Questions

What type of quadrilateral is a rhombus?

What is a quadrilateral?

What do the four angles in a quadrilateral add up to?

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