Line and rotational symmetry worksheet

Part A: Working out and filling in

1. 1. 1 line

   Try every fold, upright, across and slanting, and see each time whether the halves match exactly.

   Try every fold — upright, across, slanting: 1 of them match exactly.

2. 2. 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.

3. 3. 6 times

   Every side of a regular polygon is the same. Each time a side turns into the next one's place, it matches.

   A regular polygon's sides are all equal, so it matches every 360° ÷ 6: 6 times in a whole turn.

4. 4. 4 times

   Imagine turning it slowly and count each time it looks the same, until one whole turn is done.

   It matches every 360° ÷ 4: 4 times in a whole turn.

5. 5. 72°

   First count how many times it matches in a whole turn, then divide 360° by that.

   It matches 5 times in a whole turn: 360 ÷ 5 = 72°.

6. 6. 18°

   A regular polygon with 20 sides matches itself how many times in a whole turn?

   It matches 20 times in a whole turn: 360 ÷ 20 = 18°.

Part B: Choose, or true or false

1. 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 8 lines of symmetry.

2. 8. A

   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.

3. 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.

4. 10. A

   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.

5. 11. True

   Before a whole turn (360°), is there any moment when it looks exactly the same?

   It has rotational symmetry only if it matches before a whole turn; this one matches 2 times in one turn.

6. 12. D

   The top-left pattern turned 90° goes to the top right, then the bottom right. Check each corner of each picture.

   Draw it after each 90° turn: all four corners come from the same pattern, turned.

Part C: Word problems

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

1. 13. 10 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: 5 × 2 = 10.

2. 14. 21 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: 9 × 2 = 18; the body's are counted once: 18 + 3 = 21.

3. 15. 12 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: 3 × 4 = 12.

4. 16. 9 times

   It matches every 40°. How many lots of 40° are there in 360°?

   It matches every 40°: 360 ÷ 40 = 9.

5. 17. 30°

   With 12 evenly spread sails, how many times does it match in a whole turn? Divide 360° by that.

   12 evenly spread sails match 12 times in a whole turn: 360 ÷ 12 = 30°.

6. 18. 24 times

   In one whole turn, how many times do the blades look as they did at the start?

   3 matches a turn, so 8 turns make 3 × 8 = 24.