Shape and space · Ages 11–12

Line symmetry worksheet

Part of: Line and rotational symmetry

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Shape and space · Ages 11–12

Numsprite
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Name:Date:Score:／44

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

11.Chi-keung folds a sheet of paper in half and cuts 6 holes through the folded paper, none on the fold. How many holes are there when it is opened?
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12.A butterfly pattern has line symmetry. Its left wing has 3 spots, and its body, right on the line of symmetry, has 4. How many spots does the whole butterfly have?
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13.Ka-lok folds a square sheet in half, then in half again (the two folds at right angles), and cuts 7 holes, none on a fold. How many holes are there when it is opened?
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14.Ming folds a square sheet in half, then in half again (the two folds at right angles), and cuts 9 holes, none on a fold. How many holes are there when it is opened?
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15.Ka-yan folds a sheet of paper in half and cuts 11 holes through the folded paper, none on the fold. How many holes are there when it is opened?
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16.A butterfly pattern has line symmetry. Its left wing has 12 spots, and its body, right on the line of symmetry, has 1. How many spots does the whole butterfly have?
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Show the answers and working

Line symmetry worksheet: Answers and working

1. 5 lines
Try every fold, upright, across and slanting, and see each time whether the halves match exactly.
Try every fold — upright, across, slanting: 5 of them match exactly.
2. 7 lines
In a regular polygon all sides and angles are equal. Think how many lines a square has, then one with 7 sides.
A regular polygon's sides and angles are all equal: as many lines of symmetry as sides, 7.
3. 6 lines
In a regular polygon all sides and angles are equal. Think how many lines a square has, then one with 6 sides.
A regular polygon's sides and angles are all equal: as many lines of symmetry as sides, 6.
4. 8 lines
In a regular polygon all sides and angles are equal. Think how many lines a square has, then one with 8 sides.
A regular polygon's sides and angles are all equal: as many lines of symmetry as sides, 8.
5. 5 lines
In a regular polygon all sides and angles are equal. Think how many lines a square has, then one with 5 sides.
A regular polygon's sides and angles are all equal: as many lines of symmetry as sides, 5.
6. 10 lines
In a regular polygon all sides and angles are equal. Think how many lines a square has, then one with 10 sides.
A regular polygon's sides and angles are all equal: as many lines of symmetry as sides, 10.

7. True
Try to find a line to fold along: can the two halves match exactly?
It has line symmetry only if a fold makes the halves match; this one has 1 lines of symmetry.
8. D
Try folding each shape: can you find a line where the two halves match exactly?
Only it folds along a line so that the halves match exactly.
9. C
For each square on one side, count how far it is from the dashed line; its partner must be just as far on the other side.
Each square and its partner are the same distance from the line, flipped left to right.
10. D
The line runs across, so each square's partner is flipped top to bottom, just as far from the line.
The line is across, so each square's partner is flipped top to bottom, the same distance from it.

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

11. 12 holes
The paper is folded in half: how many layers does each hole go through?
Each cut goes through two layers, the fold being the line of symmetry: 6 × 2 = 12.
12. 10 spots
The right wing has as many spots as the left. The body is on the line, so how many times are its spots counted?
The right wing matches the left: 3 × 2 = 6; the body's are counted once: 6 + 4 = 10.
13. 28 holes
After two folds, how many layers are there? Each hole goes through all of them.
Two folds make 4 layers, both folds lines of symmetry: 7 × 4 = 28.
14. 36 holes
After two folds, how many layers are there? Each hole goes through all of them.
Two folds make 4 layers, both folds lines of symmetry: 9 × 4 = 36.
15. 22 holes
The paper is folded in half: how many layers does each hole go through?
Each cut goes through two layers, the fold being the line of symmetry: 11 × 2 = 22.
16. 25 spots
The right wing has as many spots as the left. The body is on the line, so how many times are its spots counted?
The right wing matches the left: 12 × 2 = 24; the body's are counted once: 24 + 1 = 25.

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