KS3 Maths · Year 7 · Chapter 2: Geometry · Lesson 1

Parallel lines

Year 7About 60 minutesNo calculator45 marks

Hints online, answers free with an account:
mathswariz.uk/worksheets/ks3-year-7-parallel-lines/

Date

Do Now

Quick questions to start.

A1
Needed today
Solve $3 x + 25 = 160$ .
[1 mark]
Answer
A2
Needed today
Work out $180 - 53 - 64$ .
[1 mark]
Answer
A3
From chapter 1
Work out $(- 8) \times (- 7)$ .
[1 mark]
Answer
A4
Last lesson
Write $60$ as a product of prime factors.
[1 mark]
Answer

Example, then your turn

Year 7

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

Example 1

The two lines are parallel. Work out the sizes of angles $a$ , $b$ and $c$ . Give a reason for each.

Not drawn accurately

Hint Use one fact at a time: a straight line, then alternate, then corresponding angles.

B1
The two lines are parallel. Work out the sizes of angles $p$ , $q$ and $r$ . Give a reason for each.
[3 marks]
Not drawn accurately
Answer $p = \dots \dots^{\circ}$ $q = \dots \dots^{\circ}$ $r = \dots \dots^{\circ}$

Example 2

The two lines are parallel. Work out the value of $x$ and the size of each marked angle.

Not drawn accurately

Hint The angles make a Z shape: they are alternate angles, so they are equal.

B2
The two lines are parallel. Work out the value of $x$ .
[2 marks]
Not drawn accurately
Answer

Example 3

The two lines are parallel. Work out the value of $x$ and the size of each marked angle.

Not drawn accurately

Hint Both angles are between the lines, on the same side: co-interior (allied) angles add up to

18 0^{\circ}

B3
The two lines are parallel. Work out the value of $x$ and the size of each marked angle.
[3 marks]
Not drawn accurately
Answer $x = \dots\dots$ angles $\dots \dots^{\circ}$ and $\dots \dots^{\circ}$

Example 4

The line through $A$ is parallel to $B C$ . Prove that the angles of triangle $A B C$ add up to $18 0^{\circ}$ : $a + b + c = 18 0^{\circ}$ .

Not drawn accurately

Hint Find two angles on the line through

A

that equal

b

and

c

B4
In triangle $A B C$ the side $B C$ is extended to $D$ . Use the result of the example to prove that the exterior angle $d$ is equal to $a + b$ .
[3 marks]
Not drawn accurately

Practice

Year 7

C1
The two lines are parallel. Write down the letter of the angle that is (i) alternate to $a$ , (ii) corresponding to $b$ , (iii) co-interior (allied) with $a$ .
[3 marks]
Answer(i) $\dots$ (ii) $\dots$ (iii) $\dots$
C2
The two lines are parallel. Work out the value of $x$ .
[2 marks]
Not drawn accurately
Answer

C3
A straight line crosses two other lines. Are the two lines parallel? Give a reason for your answer.
[2 marks]
Not drawn accurately
Answer
C4
$A B C D$ is a parallelogram. Angle $A = 7 1^{\circ}$ . Work out the sizes of angles $B$ , $C$ and $D$ .
[3 marks]
Not drawn accurately
Answer $B = \dots \dots^{\circ}$ $C = \dots \dots^{\circ}$ $D = \dots \dots^{\circ}$

Exam-style questions

GCSE Foundation

D1
The two lines are parallel. Write down the size of the angle marked $x$ . Give a reason for your answer.
[2 marks]
Not drawn accurately
Answer $x = \dots \dots^{\circ}$

D2
Leah says, "Angle $y$ is $6 4^{\circ}$ , because alternate angles are equal."
The two lines are parallel. Is Leah correct? Explain your answer.
[2 marks]
Not drawn accurately
D3
$D A E$ is a straight line, parallel to $B C$ . Angle $D A B = 5 7^{\circ}$ and angle $B A C = 6 4^{\circ}$ . Work out the size of angle $A C B$ . Give reasons for your answer.
[4 marks]
Not drawn accurately
Answer
D4
The two lines are parallel.
Not drawn accurately
(a)
Work out the value of $x$ .
[3 marks]
Answer
(b)
Work out the size of angle $y$ . Give a reason for your answer.
[2 marks]
Answer
Total for D4: 5 marks
D5
$A B C D$ is a trapezium. $A B$ is parallel to $D C$ . Work out the value of $y$ .
[3 marks]
Not drawn accurately
Answer

Extension

Stretch

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

E1
$A B$ is parallel to $D E$ . Angle $B A C = 13 6^{\circ}$ and angle $C D E = 15 1^{\circ}$ . Work out the size of angle $A C D$ . Give reasons for your working.
[4 marks]
Not drawn accurately
Hint 1 · What to try
Draw a line through $C$ parallel to $A B$ .
Hint 2 · The first line
The angle between that line and $C A$ is co-interior with $13 6^{\circ}$ , so it is $180 - 136 = 4 4^{\circ}$ .
Hint 3 · The full method
The other part is $180 - 151 = 2 9^{\circ}$ , so angle $A C D = 44 + 29 = 7 3^{\circ}$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can spot alternate, corresponding and co-interior (allied) angles.
I can find angles at parallel lines and give the reason.
I can write and solve an equation from angles at parallel lines.

Answers and mark scheme

The worked answers and the full mark scheme are free with a Mathswariz account. Teachers and students can both sign up.

Get the answers