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Quadrilateral Properties

In this worksheet, students remind themselves of the geometrical properties of quadrilaterals for their work with Pythagoras' Theorem.

'Quadrilateral Properties' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Apply Pythagoras' Theorem and Trigonometric Ratios to Find Angles and Lengths in 2D Figures

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

A quadrilateral is a four-sided figure with an interior angle sum of 360º.

 

Parallelogram

Opposite sides are equal and parallel.

Opposite angles are equal.

Diagonals bisect each other.

Rotational symmetry of order 2.

No line symmetry.

 

Rectangle

 

Opposite sides are equal and parallel.

All angles are right angles.

Diagonals are equal and bisect each other.

Two axes of symmetry.

Rotational symmetry of order 2.

 

Rhombus

 

All sides are equal.

Opposite sides are parallel.

Opposite angles are equal.

Diagonals bisect each other at right angles.

Two axes of symmetry.

Rotational symmetry of order 2.

 

Square

 

All sides are equal.

Opposite sides are parallel.

All angles are right angles.

Diagonals are equal and bisect each other at right angles.

Four axes of symmetry.

Rotational symmetry of order 4.

 

Kite

 

Two pairs of adjacent sides are equal.

Diagonals cut each other at right angles.

One diagonal is bisected by the other.

One axis of symmetry.

No rotational symmetry.

 

Trapezium

One pair of opposite sides is parallel

 

Isosceles Trapezium

.

One pair of opposite sides is parallel.

The non-parallel sides are equal.

Two pairs of adjacent equal angles.

One line of symmetry.

 

(In this worksheet, always give the most general answer.  This means that if a square and a rectangle fit the bill, you should write rectangle).

ABCD is a quadrilateral.

 

AB is parallel to CD and the diagonals are of equal length.

 

What type of quadrilateral is it?

Parallelogram

Rectangle

Rhombus

Square

Kite

Trapezium

Isosceles trapezium

ABCD is a quadrilateral.

 

AB is parallel to CD.  ∠A = ∠C.

 

What type of quadrilateral is it?

Parallelogram

Rectangle

Rhombus

Square

Kite

Trapezium

Isosceles trapezium

ABCD is a quadrilateral.

 

AB = BC and ∠A = ∠C = 90º.

 

What type of quadrilateral is it?

Parallelogram

Rectangle

Rhombus

Square

Kite

Trapezium

Isosceles trapezium

ABCD is a quadrilateral.

 

AC is a line of symmetry and ∠A = ∠C = 90º.

 

What type of quadrilateral is it?

Parallelogram

Rectangle

Rhombus

Square

Kite

Trapezium

Isosceles trapezium

ABCD is a quadrilateral.

 

AB is parallel to CD but AB ≠ CD. However BC = AD.

 

What type of quadrilateral is it?

Parallelogram

Rectangle

Rhombus

Square

Kite

Trapezium

Isosceles trapezium

ABCD is a parallelogram.

 

AC is perpendicular to BD but AC ≠ BD.

 

What type of quadrilateral is it?

Parallelogram

Rectangle

Rhombus

Square

Kite

Trapezium

Isosceles trapezium

ABCD is a parallelogram.

 

AC is not perpendicular to BD but AC = BD.

 

What type of quadrilateral is it?

Parallelogram

Rectangle

Rhombus

Square

Kite

Trapezium

Isosceles trapezium

ABCD is a parallelogram.

 

AC is perpendicular to BD and AC = BD.

 

What type of quadrilateral is it?

Parallelogram

Rectangle

Rhombus

Square

Kite

Trapezium

Isosceles trapezium

ABCD is a quadrilateral.

 

AC and BD cut each other at right angles at the point X, where AX = XC.

 

What type of quadrilateral is it?

Parallelogram

Rectangle

Rhombus

Square

Kite

Trapezium

Isosceles trapezium

ABCD is a quadrilateral.

 

Four congruent right-angled triangles are formed by the sides and the diagonals.

 

What type of quadrilateral is it?

Parallelogram

Rectangle

Rhombus

Square

Kite

Trapezium

Isosceles trapezium

  • Question 1

ABCD is a quadrilateral.

 

AB is parallel to CD and the diagonals are of equal length.

 

What type of quadrilateral is it?

CORRECT ANSWER
Isosceles trapezium
  • Question 2

ABCD is a quadrilateral.

 

AB is parallel to CD.  ∠A = ∠C.

 

What type of quadrilateral is it?

CORRECT ANSWER
Parallelogram
  • Question 3

ABCD is a quadrilateral.

 

AB = BC and ∠A = ∠C = 90º.

 

What type of quadrilateral is it?

CORRECT ANSWER
Kite
  • Question 4

ABCD is a quadrilateral.

 

AC is a line of symmetry and ∠A = ∠C = 90º.

 

What type of quadrilateral is it?

CORRECT ANSWER
Square
  • Question 5

ABCD is a quadrilateral.

 

AB is parallel to CD but AB ≠ CD. However BC = AD.

 

What type of quadrilateral is it?

CORRECT ANSWER
Isosceles trapezium
  • Question 6

ABCD is a parallelogram.

 

AC is perpendicular to BD but AC ≠ BD.

 

What type of quadrilateral is it?

CORRECT ANSWER
Rhombus
  • Question 7

ABCD is a parallelogram.

 

AC is not perpendicular to BD but AC = BD.

 

What type of quadrilateral is it?

CORRECT ANSWER
Rectangle
  • Question 8

ABCD is a parallelogram.

 

AC is perpendicular to BD and AC = BD.

 

What type of quadrilateral is it?

CORRECT ANSWER
Square
  • Question 9

ABCD is a quadrilateral.

 

AC and BD cut each other at right angles at the point X, where AX = XC.

 

What type of quadrilateral is it?

CORRECT ANSWER
Kite
  • Question 10

ABCD is a quadrilateral.

 

Four congruent right-angled triangles are formed by the sides and the diagonals.

 

What type of quadrilateral is it?

CORRECT ANSWER
Rhombus
---- OR ----

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