Shape and space · Ages 8–9
Parallel lines, quadrilaterals and triangles worksheet
Covers: Parallel lines, Parallelograms and trapeziums, Kinds of triangle, Three sides of a triangle, Curve stitching, Colouring a map
In the print window, choose “Save as PDF” to download it. The answers print on the last page.
Parallel lines, quadrilaterals and triangles worksheet
Shape and space · Ages 8–9
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.Two parallel lines are 14 cm apart in one place. How far apart are they in another place?
Answer:
2.Two neighbouring sides of a parallelogram are 12 cm and 19 cm. How long is the side opposite the 12 cm side?
Answer:
3.How many pairs of opposite sides of the quadrilateral on the dot paper are parallel?
Answer:
4.Lines are drawn from the top corner of the big triangle down to its base. How many triangles are there in the picture altogether?
Answer:
5.Two sticks are 7 cm and 12 cm. To make a triangle, what is the shortest the third stick can be, in whole centimetres?
Answer:
6.In curve stitching the upright arm and the flat arm each have 10 points. Each thread joins a point on one arm to a point on the other, and every point gets one thread. How many threads are there?
Answer:
7.In curve stitching every point on the arms gets one thread (a few are drawn). How many threads are there when it is finished?
Answer:
8.The outer regions of this map make a ring, and the middle region touches every one of them. Neighbouring regions need different colours. What is the fewest colours needed?
Answer:
9.The regions of this map make a ring round a lake, which isn't coloured. Neighbouring regions need different colours. What is the fewest colours needed?
Answer:
Part B: Choose, or true or false (2 marks each)
10.The two segments in the picture are parallel.
True or false?
Answer:
11.What kind of triangle is this? (Choose the most exact name.)
- A. Isosceles right-angled
- B. Equilateral
- C. Right-angled
- D. Isosceles
Choose the right answer
Answer:
12.Sticks of 6 cm, 12 cm and 8 cm can make a triangle.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.Chi-keung draws a segment on dot paper: 3 right and 1 down. Chi-keung wants a parallel segment 2 times as long, and draws 6 squares right. How many squares down must it go?
Working:
Answer:
14.A board is a trapezium. Its upper base is 36 cm, its lower base is 3 cm longer, and each leg is 7 cm. How long are its four sides altogether?
Working:
Answer:
15.An isosceles flower bed has sides adding up to 22 m, with a base of 8 m. How long is each leg?
Working:
Answer:
16.Tsz-ching has straws of 5 cm and 5 cm and wants to cut a third to make a triangle. What is the longest the third can be, in whole centimetres?
Working:
Answer:
17.Ka-yan does curve stitching with 6 points on each arm, each point getting a thread. Ka-yan stitches 2 threads a minute. How many minutes does it take?
Working:
Answer:
18.A park has 10 flower beds in a ring, each next to the two beside it. Neighbouring beds need flowers of different colours. What is the fewest colours needed?
Working:
Answer:
Show the answers and working
Parallel lines, quadrilaterals and triangles worksheet: Answers and working
Part A: Working out and filling in
1. 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.
2. 12 cm
How are a parallelogram's opposite sides related? Find the side opposite the 12 cm one.
A parallelogram's opposite sides are equal: 12 cm.
3. 1 pair
Compare the moves of the top and bottom sides first, then of the left and right sides.
Opposite sides are parallel when their moves match: 1 pair(s).
4. 6 triangles
Count the smallest triangles first, then those made of two next to each other, and so on. Don't forget the biggest one.
There are 3 smallest triangles; then count those made of two, three, … side by side, the biggest one too: 6 in all.
5. 6 cm
The third must be longer than the difference between 7 and 12. Work out that difference first.
It must be longer than the difference, 5: at least 6 cm.
6. 10 threads
Each thread uses one point on the upright arm. However many points it has, that is how many threads.
Each thread uses one point on each arm, and each arm has 10 points: 10 threads.
7. 4 threads
Count the points on one arm. Each thread joins one point on each arm.
Each arm has 4 points and each thread joins one point on each arm: 4 threads.
8. 4 colours
First work out the colours for the ring alone. The middle touches every ring region: can it share any of their colours?
The ring of 9 needs 4 − 1 colours, and the middle touches them all, so 1 more: 4.
9. 2 colours
Count the regions in the ring, then take turns with two colours all the way round. Is there a clash back at the start?
The ring has 6 regions: an even number takes turns with 2; an odd number clashes on the way round and needs 3.
Part B: Choose, or true or false
10. True
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.
11. A. Isosceles right-angled
Find the right-angle mark first, then check whether the two sides beside it are the same length.
It has a right angle; the sides beside it are 3 and 3 cm — equal means isosceles right-angled.
12. True
Find the longest of 6, 12 and 8 first, then add the other two and compare with it.
Any two sticks together must be longer than the third. 6 + 12 and 8 + 12 both beat the stick left over, so it comes down to 6 + 8 = 14: it must be longer than 12.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 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.
14. 89 cm
Find the lower base first: 3 cm longer than the 36 cm upper base. Then add all four sides.
Bottom base 36 + 3 = 39; 36 + 39 + 7 + 7 = 89.
15. 7 m
Take the 8 m base from 22 m first to find how long the two legs are together.
The two legs make 22 − 8; each is half: 7 m.
16. 9 cm
The third must be shorter than the other two together. Work out 5 + 5 first.
Shorter than 5 + 5: at most 9 cm.
17. 3 minutes
First work out how many threads there are in all: each arm has 6 points.
6 threads: 6 ÷ 2 = 3 minutes.
18. 2 colours
The beds make a ring. Is 10 odd or even? Try taking turns with two colours all the way round.
A ring of 10: an even number manages with 2 taking turns; an odd number needs 3.
Numsprite · numsprite.com/en/worksheets/parallel-lines-quadrilaterals-and-triangles
Practise it in the gameParallel lines, quadrilaterals and triangles · Unlimited questions, no download