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5 2D shapes
5.1 Quadrilaterals
bisect decompose
Worked example 1 diagonal justify
I am a quadrilateral. All my sides are equal in length. parallel trapezia
None of my angles are 90°. I have two pairs of
equal angles. What shape am I?
Square or rhombus … All sides are equal in length.
Cannot be square … No angles are 90°.
Must be a rhombus. Two pairs of equal angles.
Exercise 5.1
kite rhombus square
Focus
parallelogram trapezium
1 Name each of these special quadrilaterals.
All the names are in the box. rectangle isosceles trapezium
a b c
d e f g
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5.1 Quadrilaterals
2 Complete these properties of a kite. There is a diagram to help you.
a It has pairs of equal sides.
b It has pair of equal angles.
c The diagonals cross each other at °.
d It has line of symmetry.
3 Complete these properties of a rhombus.
There are some diagrams to help you.
a It has equal sides.
b It has pairs of equal angles.
c It has pairs of parallel sides.
d The diagonals bisect each other at °.
e It has lines of symmetry.
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5 2D shapes
Practice
4 Write down the name of the shape being described.
a I am a quadrilateral. All my sides are different lengths.
Two of my sides are parallel.
I am a .
b I am a quadrilateral. All my sides meet at right angles.
My diagonals bisect each other, but not at 90°. I am a .
c I am a quadrilateral. I have two pairs of parallel sides,
two pairs of equal sides and two pairs of equal angles.
None of my angles are 90°. I am a .
5 Jake draws this rhombus and kite. He labels the lines that make the
shapes a, b, c, d and e, f, g and h. He draws the shapes so that b is
parallel to h, and the angles marked x are the same size.
e X h
a X d
f g
b c
Write true or false for each of these statements. Justify your answer.
i b is parallel to d
ii h is parallel to f
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5.1 Quadrilaterals
iii d is parallel to h
iv a is parallel to e
6 Draw a diagram to show how an isosceles trapezium can tessellate.
Challenge
7 a Describe the similarities between a rectangle and a parallelogram.
b Describe the differences between an isosceles trapezium and a kite.
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5 2D shapes
8 Put the shapes a to f through this classification flow chart and
write down the letter where each shape comes out. For example,
when you start with the square, you end at the letter H.
Start
Yes Diagonals meet No
at 90°?
Yes One pair of No Yes Two lines of No
equal angles? symmetry?
G J
Yes No No One pair of Yes
All angles 90°? parallel sides?
H I K L
a Square b Rectangle
c Rhombus d Parallelogram
e Kite f Isosceles trapezium
9 A, B and C are three points shown on this grid. D is another point on the grid.
y
10
9
8
A B
7
6
5
4
C
3
2
1
0
x
0 1 2 3 4 5 6 7 8 9 10
a When D is at (7, 4) is quadrilateral ABDC a square? Explain your answer.
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5.2 Circles
b Point D moves so that quadrilateral ABCD is a parallelogram.
What are the coordinates of point D?
c Point D moves so that quadrilateral ABDC is a kite.
Write down two possible sets of coordinates for the point D.
5.2 Circles
Worked example 1 centre circumference
Label the parts of this circle. compasses diameter
radius
Circumference is
radius
the perimeter.
Centre is in the
circumference
middle.
Radius is the
distance from
the centre to the
centre
circumference.
diameter Diameter is the
distance across
the circle, going
through the centre.
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5 2D shapes
Exercise 5.2
Focus
1 This is how Tami labelled the parts of a circle.
radius
circumference
diameter
centre
Explain the mistakes she has made.
2 Measure the radius of each of these circles.
a
radius = cm
b
radius = mm
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5.2 Circles
3 Draw a circle with a radius of
a 3 cm b 40 mm
Practice
4 Draw a circle with a radius of
a 3.7 cm b 52 mm
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5 2D shapes
5 Write true or false for each of these statements.
a A radius of 5 cm is the same as a diameter of 10 cm.
b A diameter of 6 cm is the same as a radius of 12 cm.
c A radius of 70 mm is the same as a radius of 7 cm.
d A radius of 45 mm is the same as a diameter of 9 cm.
6 a Draw a dot and label the point C.
Make sure there is about 5 cm of space above, below, to the left
and to the right of your point.
b Draw the set of points that are exactly 4.2 cm from the point C.
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5.2 Circles
Challenge
7 a Draw a circle with radius 7 cm. Label the circle A.
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5 2D shapes
b Draw a circle with radius 3 cm, inside circle A so that it touches circle A.
Label the circle B.
Your diagram should look something like this.
A B
B A
or
c With a ruler, accurately measure the distance between the centre
of circle A and the centre of circle B.
d What do you notice about your answer to part c and the radii
measurements of circles A and B?
e Draw two more circles that touch inside. Choose your own radii
measurements. Measure the distance between the centres of
your two circles. What do you notice?
f Complete this general rule:
The distance between the centres of two touching circles that touch
inside is the same as the .
8 Zara wants to draw a pattern made of squares inside circles like this.
Step 1: Draw a square.
Step 2: Guess where the centre
of the square is and mark a dot.
Put the point of the compasses on this dot
and open the compasses so that the pencil
This is the method she uses to
is on a corner of the square.
draw one of the squares in a circle.
Step 3: Draw a circle. If the corners of the
square don’t touch the circle, rub the
circle out and try again with a
different centre point!
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5.2 Circles
a Try to draw a square in a circle using Zara’s method.
What do you think of her method?
b Can you improve on her method? If you can think of a better method,
write it down.
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5 2D shapes
5.3 Rotational symmetry
Worked example 3 order
Use tracing paper to work out the order of rotational rotational symmetry
symmetry of a rectangle.
Step 1: Trace the shape.
Step 2: Put your pencil on the centre of
the shape.
Step 3: Turn the tracing paper one full turn and count the number of
times the shape fits on itself.
Start Once Twice
The rectangle fits on itself twice, so it has order 2.
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5.3 Rotational symmetry
Exercise 5.3
Focus
1 Use tracing paper to work out the order of rotational symmetry
of these shapes.
a b c
d e f
2 Match each shape to its order of rotational symmetry.
a b c d
i Order 4 ii Order 2 iii Order 1 iv Order 3
3 a Draw the line of symmetry on to the triangle.
b Write down the order of rotational symmetry of the triangle.
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5 2D shapes
Practice
4 Write down the order of rotational symmetry of these shapes.
a b
c d
5 Write down the order of rotational symmetry of these patterns.
a b c
6 Write down the order of rotational symmetry of these road signs.
a b c
Challenge
7 Write the letter of each shape in the correct space.
Shape A has been done for you.
Number of lines of symmetry
0 1 2 3 4
Order of rotational 2
symmetry 3
4 A
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5.3 Rotational symmetry
A B
C D
E F
8 Mali is making a pattern from grey and white squares.
This is what she has drawn so far.
a On this copy shade in one more square so that
the pattern has order 2 rotational symmetry.
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5 2D shapes
b On this copy shade in five more squares so that the pattern
has order 4 rotational symmetry.
c On this copy shade in seven more squares so that the
pattern has order 2 rotational symmetry.
9 Sadik has these nine squares.
He wants to arrange the squares to form a square pattern with two lines of
symmetry and rotational symmetry order 2. Show two ways that he can do this.
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