Shape and space · Ages 8–9

Parallel lines worksheet

Part of: Parallel lines, quadrilaterals and triangles

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Shape and space · Ages 8–9

Numsprite
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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.On dot paper, a segment goes 5 squares right and 1 squares down. A segment parallel to it also goes 5 squares right. How many squares down must it go?
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2.Two parallel lines are 14 cm apart in one place. How far apart are they in another place?
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3.Two parallel lines are 3 cm apart in one place. How far apart are they in another place?
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4.On dot paper, a segment goes 3 squares right and 4 squares down. A segment parallel to it also goes 3 squares right. How many squares down must it go?
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5.Two parallel lines are 13 cm apart in one place. How far apart are they in another place?
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6.On dot paper, a segment goes 6 squares right and 5 squares down. A segment parallel to it also goes 6 squares right. How many squares down must it go?
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7.Segment A goes 2 right and 1 down. Segment B is parallel to A and twice as long, going 4 right. How many squares down does B go?
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8.Segment A goes 1 right and 3 down. Segment B is parallel to A and twice as long, going 2 right. How many squares down does B go?
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9.Segment A goes 4 right and 2 down. Segment B is parallel to A and twice as long, going 8 right. How many squares down does B go?
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13.The rungs of a ladder are parallel, 36 cm apart. The ladder has 6 rungs. How far is the top rung from the bottom one?
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14.May draws a segment on dot paper: 4 right and 1 down. May wants a parallel segment 2 times as long, and draws 8 squares right. How many squares down must it go?
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15.The two rails of a railway are parallel. In one place they are 159 cm apart. How far apart are they 12 m further on?
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16.The two rails of a railway are parallel. In one place they are 102 cm apart. How far apart are they 17 m further on?
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17.Ming draws a segment on dot paper: 3 right and 1 down. Ming wants a parallel segment 2 times as long, and draws 6 squares right. How many squares down must it go?
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18.The rungs of a ladder are parallel, 25 cm apart. The ladder has 9 rungs. How far is the top rung from the bottom one?
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Show the answers and working

Parallel lines worksheet: Answers and working

1. 1 square
Parallel segments make exactly the same moves. The first goes 5 right and 1 down.
Parallel segments move the same way: 1 down as well.
2. 14 cm
Think about parallel lines: they never meet however far they go. Does the gap between them ever change?
Parallel lines are the same distance apart everywhere: 14 cm.
3. 3 cm
Think about parallel lines: they never meet however far they go. Does the gap between them ever change?
Parallel lines are the same distance apart everywhere: 3 cm.
4. 4 squares
Parallel segments make exactly the same moves. The first goes 3 right and 4 down.
Parallel segments move the same way: 4 down as well.
5. 13 cm
Think about parallel lines: they never meet however far they go. Does the gap between them ever change?
Parallel lines are the same distance apart everywhere: 13 cm.
6. 5 squares
Parallel segments make exactly the same moves. The first goes 6 right and 5 down.
Parallel segments move the same way: 5 down as well.
7. 2 squares
B goes 4 right. How many times A's 2 is that? The squares down must grow the same way.
Twice as long means twice as far both ways: 1 × 2 = 2 squares.
8. 6 squares
B goes 2 right. How many times A's 1 is that? The squares down must grow the same way.
Twice as long means twice as far both ways: 3 × 2 = 6 squares.
9. 4 squares
B goes 8 right. How many times A's 4 is that? The squares down must grow the same way.
Twice as long means twice as far both ways: 2 × 2 = 4 squares.

10. B
In each picture, count how far each segment goes across and down. The two must make the same moves.
Both segments go 2 across and 1 down — the same moves — so they are parallel.
11. False
Count the first segment's squares across and down, then the second's, and compare.
Count how far each segment goes across and down: only the same moves are parallel.
12. B
Imagine extending each shape's sides. In which shape can you find no pair that never meets?
A triangle's or a regular pentagon's sides all meet when extended: no parallel sides.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 180 cm
How many gaps are there between 6 rungs? Picture 3 rungs and count the gaps.
6 rungs have 5 gaps between them: 5 × 36 = 180 cm.
14. 2 squares
Parallel and 2 times as long means both the squares right and the squares down are 2 times as many.
2 times as far right means 2 times as far down: 1 × 2 = 2.
15. 159 cm
The rails are parallel. Does the gap between parallel lines change the further along you go?
Parallel lines are the same distance apart everywhere, however far along: 159 cm.
16. 102 cm
The rails are parallel. Does the gap between parallel lines change the further along you go?
Parallel lines are the same distance apart everywhere, however far along: 102 cm.
17. 2 squares
Parallel and 2 times as long means both the squares right and the squares down are 2 times as many.
2 times as far right means 2 times as far down: 1 × 2 = 2.
18. 200 cm
How many gaps are there between 9 rungs? Picture 3 rungs and count the gaps.
9 rungs have 8 gaps between them: 8 × 25 = 200 cm.

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