Shape and space · Ages 8–9

How many lines of symmetry a shape has worksheet

Part of: Symmetry

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Shape and space · Ages 8–9

Numsprite
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Name:Date:Score:／48

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

1.How many lines of symmetry does this shape have?
Answer:
2.A regular polygon has 6 sides. Of its lines of symmetry, pass through two opposite corners and through the middles of two opposite sides.
Fill in each blank
Answer:
3.A regular polygon has 14 sides. Of its lines of symmetry, pass through two opposite corners and through the middles of two opposite sides.
Fill in each blank
Answer:
4.A regular polygon has 18 sides. Of its lines of symmetry, pass through two opposite corners and through the middles of two opposite sides.
Fill in each blank
Answer:
5.A regular polygon has 4 sides. Of its lines of symmetry, pass through two opposite corners and through the middles of two opposite sides.
Fill in each blank
Answer:

13.Ka-yee has 2 square sheets of paper and 5 rectangular sheets (length and width not equal). Ka-yee folds every sheet once along each of its lines of symmetry. How many folds is that altogether?
Working:
Answer:
14.Ming has a coaster shaped like a regular polygon with 7 sides. How many different ways can it be folded along a straight line so that the two halves match exactly?
Working:
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15.A round pizza is to be cut once along a straight line into two halves exactly alike. How many different ways are there to cut it?
- A. Infinitely many
- B. 2
- C. 1
- D. 4
Choose the right answer
Working:
Answer:
16.Ka-lok has 4 square sheets of paper and 5 rectangular sheets (length and width not equal). Ka-lok folds every sheet once along each of its lines of symmetry. How many folds is that altogether?
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17.Tsz-ching has 2 square sheets of paper and 4 rectangular sheets (length and width not equal). Tsz-ching folds every sheet once along each of its lines of symmetry. How many folds is that altogether?
Working:
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18.Tsz-hin has a coaster shaped like a regular polygon with 8 sides. How many different ways can it be folded along a straight line so that the two halves match exactly?
Working:
Answer:

Show the answers and working

How many lines of symmetry a shape has worksheet: Answers and working

1. 5 lines
Try every fold: upright, flat and slanting. Keep a count of each one where the halves match.
Try every fold, upright, flat and slanting: 5 of them match exactly.
2. 3, 3
6 is even, so every corner has an opposite corner. How many pairs do 6 corners make?
6 is even: its 6 corners make 3 opposite pairs and its 6 sides 3 more, 6 lines in all.
3. 7, 7
14 is even, so every corner has an opposite corner. How many pairs do 14 corners make?
14 is even: its 14 corners make 7 opposite pairs and its 14 sides 7 more, 14 lines in all.
4. 9, 9
18 is even, so every corner has an opposite corner. How many pairs do 18 corners make?
18 is even: its 18 corners make 9 opposite pairs and its 18 sides 9 more, 18 lines in all.
5. 2, 2
4 is even, so every corner has an opposite corner. How many pairs do 4 corners make?
4 is even: its 4 corners make 2 opposite pairs and its 4 sides 2 more, 4 lines in all.

6. A. 4
Work out what the shape is, then try upright, flat and slanting folds. If it is a circle, think about its diameters.
Try each fold and count; a circle matches on every diameter, so it has infinitely many.
7. False
Try every fold and count this shape's lines of symmetry, then compare with 4.
Try every fold: this shape has 3 lines of symmetry.
8. D
Find all the shape's lines of symmetry yourself first, then check each picture for extra or missing lines.
Fold on each dashed line: every one must match, and every line that does match must be drawn.
9. False
Try every fold and count this shape's lines of symmetry, then compare with 3.
Try every fold: this shape has 1 lines of symmetry.
10. False
Try every fold and count this shape's lines of symmetry, then compare with 0.
Try every fold: this shape has 0 lines of symmetry.
11. False
Try every fold and count this shape's lines of symmetry, then compare with 6.
Try every fold: this shape has 5 lines of symmetry.
12. False
Try every fold and count this shape's lines of symmetry, then compare with 1.
Try every fold: this shape has 1 lines of symmetry.

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

13. 18 folds
First think how many lines of symmetry a square sheet has, and how many a rectangular one has.
A square has 4 lines and a rectangle 2: 2 × 4 + 5 × 2 = 8 + 10 = 18.
14. 7 ways
Each fold where the halves match is a line of symmetry. How many lines of symmetry does a regular polygon with 7 sides have?
Each such fold is a line of symmetry: a regular polygon with 7 sides has 7.
15. A. Infinitely many
The pizza is a circle. What kind of cut gives two halves exactly alike, and how many such lines are there?
Any cut through the centre makes two equal halves, and there are infinitely many lines through the centre.
16. 26 folds
First think how many lines of symmetry a square sheet has, and how many a rectangular one has.
A square has 4 lines and a rectangle 2: 4 × 4 + 5 × 2 = 16 + 10 = 26.
17. 16 folds
First think how many lines of symmetry a square sheet has, and how many a rectangular one has.
A square has 4 lines and a rectangle 2: 2 × 4 + 4 × 2 = 8 + 8 = 16.
18. 8 ways
Each fold where the halves match is a line of symmetry. How many lines of symmetry does a regular polygon with 8 sides have?
Each such fold is a line of symmetry: a regular polygon with 8 sides has 8.

Numsprite · numsprite.com/en/worksheets/symmetry/counting-lines-of-symmetry