 # Apply the Properties of Quadrilaterals

In this worksheet, students will learn about and apply the properties of quadrilaterals. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Geometry and Measures, Basic Geometry

Curriculum subtopic:   Properties and Constructions, Properties of Polygons

Difficulty level:   ### QUESTION 1 of 10 Ever ridden one of these?  I would love to have a go on a quad bike.

Did you know that quad means four?

This means that any four sided shape is called a quadrilateral.

There are several quadrilaterals but each have different properties (facts).  Lets see  Okay time to see what we know Which of these statements is true

 True False There is one pair of parallel sides and 1 line of symmetry There is 1 pair of parallel sides and 0 lines of symmetry How many lines of symmetry does this quadrilateral have? Which statements is true of this shape? Which quadrilateral has no lines of symmetry? 360°

270°

180°

90° Which quadrilateral has 1 line of symmetry and opposite equal angles?

Trapezium

Rhombus

Rectangle

Kite Three angles of a quadrilateral are 75°, 120°,  98°.

What is the size of the missing angle? Match up the statement to the shape

## Column B

Kite
There are 4 equal angles and four lines of symmetr...
Square
There is 1 line of symmetry and one pair of opposi...
Parallelogram
There is one set of parallel sides
Trapezium

More match up

## Column B

There are 1 or 0 lines of symmetry
Parallelogram
Rotational symmetry order 4
Square
Rotational symmetry order 2
Trapezium
No rotational symmetry
Rectangle
• Question 1 Which of these statements is true

 True False There is one pair of parallel sides and 1 line of symmetry There is 1 pair of parallel sides and 0 lines of symmetry
EDDIE SAYS
The trapezium, this can be the awkward one. If it is irregular like this one then there is no symmetry. The only thing for certain is that there is one set of parallel sides.
• Question 2 How many lines of symmetry does this quadrilateral have?

2
EDDIE SAYS
Why was your teacher late to class today? They took the rhombus. This shape often gets mixed up with the square, but their properties are quite different. The only thing they have in common is that four sides are equal.
• Question 3 Which statements is true of this shape?

EDDIE SAYS
So much to learn, so little time. This one often gets mixed up with the rectangle but it is quite different. The parallel sides are easy to spot, but the angle properties are the tricky one. The opposite angles are the ones opposite each other on the diagonal.
• Question 4 Which quadrilateral has no lines of symmetry?

irregular trapezium
EDDIE SAYS
Because you can have regular and irregular shapes you have to be careful not to think the properties are the same for both. Irregular shapes don't have lines of symmetry. The clue is in the title.... irregular
• Question 5 180°
EDDIE SAYS
The adjacent angles are the ones opposite each other (not on the diagonal). These add up to 180° So when you are given one, the other is easy to work out. Just how I like it.
• Question 6 Which quadrilateral has 1 line of symmetry and opposite equal angles?

Kite
EDDIE SAYS
Are you flying high on these now? This is probably the simplest one to remember. I think of the basic kite I had as a child and the tail coming out of the bottom is the one line of symmetry.
• Question 7 Three angles of a quadrilateral are 75°, 120°,  98°.

What is the size of the missing angle?

67
EDDIE SAYS
This is just one of the facts that we have to learn in maths. Angles in a quadrilateral add up to 360°. 360 - 75 - 120 - 98 = 67°
• Question 8 EDDIE SAYS
Are you able to separate this from a square? These two often get mixed up but the square also has symmetry on the diagonals but the rectangle doesn't.
• Question 9

Match up the statement to the shape

## Column B

Parallelogram
There are 4 equal angles and four...
Square
There is 1 line of symmetry and o...
Kite
There is one set of parallel side...
Trapezium
EDDIE SAYS
Sometimes you don't need to know all of the properties. Sometimes you are given one or two which is often the clue to working out further problems. If you are not given a picture remember, if in doubt sketch it out.
• Question 10

More match up

## Column B

There are 1 or 0 lines of symmetr...
Trapezium
Rotational symmetry order 4
Square
Rotational symmetry order 2
Rectangle
No rotational symmetry
Parallelogram
EDDIE SAYS
Did this get you in a spin? Sometimes rotational symmetry is the hardest to spot. How many times does the shape fit into itself if you turn it 360° from its centre. Quite often it is the parallelogram that causes problems, because it looks like a wonky rectangle people think there is two. Try it, the shape doesn't fit into itself when you turn it.
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