KS3 Maths · Year 7 · Chapter 2: Geometry · Lesson 2

The geometric properties of quadrilaterals

Year 7About 70 minutesNo calculator45 marks

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Quick questions to start.

A1
Needed today
Two angles of a triangle are $4 8^{\circ}$ and $7 5^{\circ}$ . Work out the third angle.
[1 mark]
Answer
A2
Needed today
Three angles of a quadrilateral are $9 0^{\circ}$ , $8 5^{\circ}$ and $11 0^{\circ}$ . Work out the fourth angle.
[1 mark]
Answer
A3
Last lesson
Two co-interior angles between parallel lines are $10 7^{\circ}$ and $x$ . Work out $x$ .
[1 mark]
Answer
A4
From chapter 1
Find the HCF of $48$ and $80$ .
[1 mark]
Answer

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

A quadrilateral has four equal sides. It has no right angles. Name the quadrilateral.

Hint Which quadrilaterals have four equal sides? Which of those has right angles?

Example 2

Write down the number of lines of symmetry and the order of rotational symmetry of a rhombus.

Hint Fold it along each diagonal. Then turn it round its centre and count how many times it fits on itself.

B2
Write down the number of lines of symmetry and the order of rotational symmetry of a parallelogram.
[2 marks]
Answerlines $\dots$ order $\dots$

Example 3

$A B C D$ is a parallelogram. Work out the sizes of the angles marked $x$ and $y$ .

Not drawn accurately

Hint Opposite angles of a parallelogram are equal. Angles next to each other add up to

18 0^{\circ}

B3
$A B C D$ is a parallelogram. Work out the sizes of the angles marked $x$ , $y$ and $z$ .
[3 marks]
Not drawn accurately
Answer $x = \dots$ $y = \dots$ $z = \dots$

Example 4

$A B C D$ is a kite. Work out the size of the angle marked $x$ .

Not drawn accurately

Hint A kite has one pair of equal angles, between the sides of different lengths. The four angles add up to

36 0^{\circ}

B4
$A B C D$ is a kite. Work out the size of the angle marked $x$ .
[2 marks]
Not drawn accurately
Answer

Year 7

C1
$A B C D$ is a rectangle. Its diagonals cross at $M$ . The diagonal $A C$ is $13$ cm long. Work out the length of $B M$ .
[2 marks]
Not drawn accurately
Answer
C2
$A B C D$ is a rhombus. Angle $A B D = 3 5^{\circ}$ . Work out angle $B A D$ .
[2 marks]
Not drawn accurately
Answer

C3
This trapezium has a line of symmetry. Work out the size of the angle marked $x$ .
[2 marks]
Not drawn accurately
Answer
C4
A quadrilateral has exactly one line of symmetry. One of its angles is more than $18 0^{\circ}$ . Name the quadrilateral.
[1 mark]
Answer
C5
A rhombus has a perimeter of $38 cm$ . Work out the length of one of its sides.
[2 marks]
Answer

GCSE Foundation

D2
Sam says, "A square is not a rhombus, because a rhombus has no right angles."
Sam is wrong. Explain why.
[2 marks]
D3
$A$ , $B$ and $C$ are three corners of a kite $A B C D$ . The line $A C$ is a line of symmetry of the kite.
(a)
Write down the coordinates of $D$ .
[2 marks]
Answer
(b)
Work out the length of the diagonal $B D$ .
[1 mark]
Answer
(c)
Work out the length of the diagonal $A C$ .
[1 mark]
Answer
Total for D3: 4 marks
D4
$A B C D$ is a trapezium. $A B$ is parallel to $D C$ . Angle $D A B = 10 5^{\circ}$ and angle $A B C = 11 8^{\circ}$ .
Not drawn accurately
(a)
Work out the size of angle $A D C$ . Give a reason for your answer.
[2 marks]
Answer
(b)
Work out the size of angle $B C D$ .
[2 marks]
Answer
Total for D4: 4 marks
D5
This rectangle is made from three identical squares in a row. The perimeter of the rectangle is $48$ cm. Work out the area of the rectangle.
[4 marks]
Answer

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can name a quadrilateral from its properties.
I can use the properties of quadrilaterals to find missing angles and lengths.
I can find a missing corner of a quadrilateral on a grid.

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