Rotational and Reflective Symmetry of Polygons worksheet for geometry practice.
Worksheet on rotational and reflective symmetry of polygons, featuring various geometric shapes like square, kite, trapezium, rhombus, rectangle, parallelogram, arrow head, equilateral triangle, regular pentagon, regular hexagon, regular octagon, and regular nonagon, with instructions to write the order of rotational symmetry and draw lines of reflective symmetry.
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Step-by-step solution for: Rotational and Refelctive Symmetry of Polygons Worksheet ...
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Show Answer Key & Explanations
Step-by-step solution for: Rotational and Refelctive Symmetry of Polygons Worksheet ...
Let's solve this step-by-step. The task is to determine the order of rotational symmetry for each shape and draw the lines of reflective symmetry.
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- The order of rotational symmetry is the number of times a shape maps onto itself when rotated around its center by 360°.
- For example, if a shape looks the same after a rotation of 90°, it has rotational symmetry of order 4 (since 360° ÷ 90° = 4).
- This refers to lines of symmetry where the shape can be folded so that both halves match perfectly.
- We need to draw all such lines.
---
We'll go through each shape:
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- Rotational Symmetry: Can rotate by 90°, 180°, 270°, 360° → Order: 4
- Lines of Reflective Symmetry: 2 diagonals + 2 midlines (vertical & horizontal) → 4 lines
✔ Draw: 2 diagonals and 2 lines through midpoints of opposite sides.
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- Rotational Symmetry: Only matches at 360° → Order: 1
- Lines of Reflective Symmetry: 1 line (along the axis from the top vertex to the bottom vertex) → 1 line
✔ Draw: One vertical line from top to bottom (through the two vertices where the equal sides meet).
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- Rotational Symmetry: Only matches at 360° → Order: 1
- Lines of Reflective Symmetry: 1 line (vertical line through midpoints of the two parallel sides) → 1 line
✔ Draw: Vertical line down the middle.
> ⚠️ Note: If it’s a non-isosceles trapezium, no reflective symmetry. But since drawn symmetrically, assume isosceles.
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- Rotational Symmetry: Rotates 180° → Order: 2
- Lines of Reflective Symmetry: 2 diagonals → 2 lines
✔ Draw: Both diagonals.
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- Rotational Symmetry: Rotates 180° → Order: 2
- Lines of Reflective Symmetry: 2 lines (vertical and horizontal midlines) → 2 lines
✔ Draw: Vertical and horizontal lines through centers.
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- Rotational Symmetry: Rotates 180° → Order: 2
- Lines of Reflective Symmetry: None → 0 lines
✔ No lines to draw.
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- Rotational Symmetry: Only matches at 360° → Order: 1
- Lines of Reflective Symmetry: 1 vertical line down the center → 1 line
✔ Draw: Vertical line through the tip and base midpoint.
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- Rotational Symmetry: Rotates 120°, 240°, 360° → Order: 3
- Lines of Reflective Symmetry: 3 lines (from each vertex to midpoint of opposite side) → 3 lines
✔ Draw: 3 medians (also altitudes and angle bisectors).
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- Rotational Symmetry: 360° ÷ 72° = Order: 5
- Lines of Reflective Symmetry: 5 lines (from each vertex to midpoint of opposite side) → 5 lines
✔ Draw: 5 lines from each vertex to the midpoint of the opposite side.
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- Rotational Symmetry: 360° ÷ 60° = Order: 6
- Lines of Reflective Symmetry: 6 lines (3 through opposite vertices, 3 through midpoints of opposite sides) → 6 lines
✔ Draw: 3 diagonals through opposite vertices, and 3 lines through midpoints of opposite sides.
---
- Rotational Symmetry: 360° ÷ 45° = Order: 8
- Lines of Reflective Symmetry: 8 lines (4 through opposite vertices, 4 through midpoints of opposite sides) → 8 lines
✔ Draw: 4 diagonals through opposite vertices, and 4 lines through midpoints of opposite sides.
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- Rotational Symmetry: 360° ÷ 40° = Order: 9
- Lines of Reflective Symmetry: 9 lines (from each vertex to midpoint of opposite side) → 9 lines
✔ Draw: 9 lines from each vertex to the midpoint of the opposite side.
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## ✔ Final Answers (Rotational Orders):
| Shape | Order of Rotational Symmetry |
|---------------------|------------------------------|
| Square | 4 |
| Kite | 1 |
| Trapezium | 1 |
| Rhombus | 2 |
| Rectangle | 2 |
| Parallelogram | 2 |
| Arrow Head | 1 |
| Equilateral Triangle| 3 |
| Regular Pentagon | 5 |
| Regular Hexagon | 6 |
| Regular Octagon | 8 |
| Regular Nonagon | 9 |
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## 🖋️ How to Draw Lines of Reflective Symmetry:
For each shape, draw:
- All lines that divide the shape into two identical mirror-image parts.
- Use a ruler and light pencil lines.
---
You should now:
1. Fill in the blanks with the rotational symmetry orders above.
2. On each shape, draw the corresponding lines of reflection using a ruler.
Let me know if you'd like a visual sketch guide or printable version!
---
🔷 What is Rotational Symmetry?
- The order of rotational symmetry is the number of times a shape maps onto itself when rotated around its center by 360°.
- For example, if a shape looks the same after a rotation of 90°, it has rotational symmetry of order 4 (since 360° ÷ 90° = 4).
🔷 What is Reflective Symmetry?
- This refers to lines of symmetry where the shape can be folded so that both halves match perfectly.
- We need to draw all such lines.
---
We'll go through each shape:
---
✔ 1. Square
- Rotational Symmetry: Can rotate by 90°, 180°, 270°, 360° → Order: 4
- Lines of Reflective Symmetry: 2 diagonals + 2 midlines (vertical & horizontal) → 4 lines
✔ Draw: 2 diagonals and 2 lines through midpoints of opposite sides.
---
✔ 2. Kite
- Rotational Symmetry: Only matches at 360° → Order: 1
- Lines of Reflective Symmetry: 1 line (along the axis from the top vertex to the bottom vertex) → 1 line
✔ Draw: One vertical line from top to bottom (through the two vertices where the equal sides meet).
---
✔ 3. Trapezium (Assuming isosceles trapezium, as typically implied in such questions)
- Rotational Symmetry: Only matches at 360° → Order: 1
- Lines of Reflective Symmetry: 1 line (vertical line through midpoints of the two parallel sides) → 1 line
✔ Draw: Vertical line down the middle.
> ⚠️ Note: If it’s a non-isosceles trapezium, no reflective symmetry. But since drawn symmetrically, assume isosceles.
---
✔ 4. Rhombus
- Rotational Symmetry: Rotates 180° → Order: 2
- Lines of Reflective Symmetry: 2 diagonals → 2 lines
✔ Draw: Both diagonals.
---
✔ 5. Rectangle
- Rotational Symmetry: Rotates 180° → Order: 2
- Lines of Reflective Symmetry: 2 lines (vertical and horizontal midlines) → 2 lines
✔ Draw: Vertical and horizontal lines through centers.
---
✔ 6. Parallelogram
- Rotational Symmetry: Rotates 180° → Order: 2
- Lines of Reflective Symmetry: None → 0 lines
✔ No lines to draw.
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✔ 7. Arrow Head
- Rotational Symmetry: Only matches at 360° → Order: 1
- Lines of Reflective Symmetry: 1 vertical line down the center → 1 line
✔ Draw: Vertical line through the tip and base midpoint.
---
✔ 8. Equilateral Triangle
- Rotational Symmetry: Rotates 120°, 240°, 360° → Order: 3
- Lines of Reflective Symmetry: 3 lines (from each vertex to midpoint of opposite side) → 3 lines
✔ Draw: 3 medians (also altitudes and angle bisectors).
---
✔ 9. Regular Pentagon
- Rotational Symmetry: 360° ÷ 72° = Order: 5
- Lines of Reflective Symmetry: 5 lines (from each vertex to midpoint of opposite side) → 5 lines
✔ Draw: 5 lines from each vertex to the midpoint of the opposite side.
---
✔ 10. Regular Hexagon
- Rotational Symmetry: 360° ÷ 60° = Order: 6
- Lines of Reflective Symmetry: 6 lines (3 through opposite vertices, 3 through midpoints of opposite sides) → 6 lines
✔ Draw: 3 diagonals through opposite vertices, and 3 lines through midpoints of opposite sides.
---
✔ 11. Regular Octagon
- Rotational Symmetry: 360° ÷ 45° = Order: 8
- Lines of Reflective Symmetry: 8 lines (4 through opposite vertices, 4 through midpoints of opposite sides) → 8 lines
✔ Draw: 4 diagonals through opposite vertices, and 4 lines through midpoints of opposite sides.
---
✔ 12. Regular Nonagon
- Rotational Symmetry: 360° ÷ 40° = Order: 9
- Lines of Reflective Symmetry: 9 lines (from each vertex to midpoint of opposite side) → 9 lines
✔ Draw: 9 lines from each vertex to the midpoint of the opposite side.
---
## ✔ Final Answers (Rotational Orders):
| Shape | Order of Rotational Symmetry |
|---------------------|------------------------------|
| Square | 4 |
| Kite | 1 |
| Trapezium | 1 |
| Rhombus | 2 |
| Rectangle | 2 |
| Parallelogram | 2 |
| Arrow Head | 1 |
| Equilateral Triangle| 3 |
| Regular Pentagon | 5 |
| Regular Hexagon | 6 |
| Regular Octagon | 8 |
| Regular Nonagon | 9 |
---
## 🖋️ How to Draw Lines of Reflective Symmetry:
For each shape, draw:
- All lines that divide the shape into two identical mirror-image parts.
- Use a ruler and light pencil lines.
---
Summary:
You should now:
1. Fill in the blanks with the rotational symmetry orders above.
2. On each shape, draw the corresponding lines of reflection using a ruler.
Let me know if you'd like a visual sketch guide or printable version!
Parent Tip: Review the logic above to help your child master the concept of lines of symmetry worksheet.
