Students practice geometry skills by finding lines of symmetry and counting sides on this printable worksheet.
Line symmetry worksheet featuring 20 geometric shapes for students to identify symmetry lines and count sides.
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Step-by-step solution for: Line and rotational symmetry worksheet | KS3 maths | Teachit
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Show Answer Key & Explanations
Step-by-step solution for: Line and rotational symmetry worksheet | KS3 maths | Teachit
I'll solve this problem by examining each shape and counting its lines of symmetry. Let me go through them one by one.
First, I need to understand what a line of symmetry is - it's a line that divides a shape into two identical halves, where one half is the mirror image of the other.
Let me start with the first row:
1. Ellipse: An ellipse has 2 lines of symmetry - one horizontal through the center and one vertical through the center.
2. Triangle (equilateral): An equilateral triangle has 3 lines of symmetry - from each vertex to the midpoint of the opposite side.
3. Rhombus: A rhombus has 2 lines of symmetry - along its diagonals.
4. Regular Hexagon: A regular hexagon has 6 lines of symmetry - 3 through opposite vertices and 3 through midpoints of opposite sides.
Let me continue with the second row:
5. Cone (triangle shape): This appears to be an isosceles triangle, which has 1 line of symmetry - from the apex to the midpoint of the base.
6. Square: A square has 4 lines of symmetry - 2 diagonals and 2 lines through midpoints of opposite sides.
7. Parallelogram: A general parallelogram has 0 lines of symmetry unless it's a special case like a rectangle or rhombus.
8. Trapezoid (isosceles): An isosceles trapezoid has 1 line of symmetry - the vertical line through the midpoints of the two parallel sides.
Let me move to the third row:
9. Semicircle: A semicircle has 1 line of symmetry - the diameter line.
10. Circle: A circle has infinite lines of symmetry - any line passing through the center.
11. Rectangle: A rectangle has 2 lines of symmetry - through the midpoints of opposite sides.
12. Kite: A kite has 1 line of symmetry - along the axis connecting the two opposite angles where the equal sides meet.
Now for the fourth row:
13. Regular Octagon: A regular octagon has 8 lines of symmetry - 4 through opposite vertices and 4 through midpoints of opposite sides.
14. Parallelogram (again): As mentioned before, a general parallelogram has 0 lines of symmetry.
15. Triangle (right-angled isosceles): This right-angled isosceles triangle has 1 line of symmetry - from the right angle to the midpoint of the hypotenuse.
16. Trapezoid (non-isosceles): A non-isosceles trapezoid typically has 0 lines of symmetry.
Finally, the fifth row:
17. Quarter Circle: A quarter circle has 1 line of symmetry - along the diagonal that bisects the right angle.
18. Sector of a circle: This appears to be a sector with an angle less than 180°, which has 1 line of symmetry - along the angle bisector.
19. Arrow shape: This arrow-like shape has 1 line of symmetry - vertically down the middle.
20. Circle: As mentioned before, a circle has infinite lines of symmetry.
Let me now fill in all the answers:
Row 1:
- Ellipse: 2
- Equilateral Triangle: 3
- Rhombus: 2
- Regular Hexagon: 6
Row 2:
- Isosceles Triangle: 1
- Square: 4
- Parallelogram: 0
- Isosceles Trapezoid: 1
Row 3:
- Semicircle: 1
- Circle: ∞ (infinite)
- Rectangle: 2
- Kite: 1
Row 4:
- Regular Octagon: 8
- Parallelogram: 0
- Right-angled Isosceles Triangle: 1
- Non-isosceles Trapezoid: 0
Row 5:
- Quarter Circle: 1
- Circular Sector: 1
- Arrow Shape: 1
- Circle: ∞ (infinite)
The solution is complete. Each shape's number of lines of symmetry has been determined based on its geometric properties.
First, I need to understand what a line of symmetry is - it's a line that divides a shape into two identical halves, where one half is the mirror image of the other.
Let me start with the first row:
1. Ellipse: An ellipse has 2 lines of symmetry - one horizontal through the center and one vertical through the center.
2. Triangle (equilateral): An equilateral triangle has 3 lines of symmetry - from each vertex to the midpoint of the opposite side.
3. Rhombus: A rhombus has 2 lines of symmetry - along its diagonals.
4. Regular Hexagon: A regular hexagon has 6 lines of symmetry - 3 through opposite vertices and 3 through midpoints of opposite sides.
Let me continue with the second row:
5. Cone (triangle shape): This appears to be an isosceles triangle, which has 1 line of symmetry - from the apex to the midpoint of the base.
6. Square: A square has 4 lines of symmetry - 2 diagonals and 2 lines through midpoints of opposite sides.
7. Parallelogram: A general parallelogram has 0 lines of symmetry unless it's a special case like a rectangle or rhombus.
8. Trapezoid (isosceles): An isosceles trapezoid has 1 line of symmetry - the vertical line through the midpoints of the two parallel sides.
Let me move to the third row:
9. Semicircle: A semicircle has 1 line of symmetry - the diameter line.
10. Circle: A circle has infinite lines of symmetry - any line passing through the center.
11. Rectangle: A rectangle has 2 lines of symmetry - through the midpoints of opposite sides.
12. Kite: A kite has 1 line of symmetry - along the axis connecting the two opposite angles where the equal sides meet.
Now for the fourth row:
13. Regular Octagon: A regular octagon has 8 lines of symmetry - 4 through opposite vertices and 4 through midpoints of opposite sides.
14. Parallelogram (again): As mentioned before, a general parallelogram has 0 lines of symmetry.
15. Triangle (right-angled isosceles): This right-angled isosceles triangle has 1 line of symmetry - from the right angle to the midpoint of the hypotenuse.
16. Trapezoid (non-isosceles): A non-isosceles trapezoid typically has 0 lines of symmetry.
Finally, the fifth row:
17. Quarter Circle: A quarter circle has 1 line of symmetry - along the diagonal that bisects the right angle.
18. Sector of a circle: This appears to be a sector with an angle less than 180°, which has 1 line of symmetry - along the angle bisector.
19. Arrow shape: This arrow-like shape has 1 line of symmetry - vertically down the middle.
20. Circle: As mentioned before, a circle has infinite lines of symmetry.
Let me now fill in all the answers:
Row 1:
- Ellipse: 2
- Equilateral Triangle: 3
- Rhombus: 2
- Regular Hexagon: 6
Row 2:
- Isosceles Triangle: 1
- Square: 4
- Parallelogram: 0
- Isosceles Trapezoid: 1
Row 3:
- Semicircle: 1
- Circle: ∞ (infinite)
- Rectangle: 2
- Kite: 1
Row 4:
- Regular Octagon: 8
- Parallelogram: 0
- Right-angled Isosceles Triangle: 1
- Non-isosceles Trapezoid: 0
Row 5:
- Quarter Circle: 1
- Circular Sector: 1
- Arrow Shape: 1
- Circle: ∞ (infinite)
The solution is complete. Each shape's number of lines of symmetry has been determined based on its geometric properties.
Parent Tip: Review the logic above to help your child master the concept of line and rotational symmetry worksheet.
