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Symmetry - Worksheet 9 - 10th Grade

Hard

Identify line and rotational symmetry in figures (Hard)

27 problems · 15-20 minutes · Skills: transformations, symmetry, geometry

About This Worksheet

This hard-level worksheet contains 27 problems designed for 10th Grade students practicing line & rotational symmetry. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Symmetry is one of the most powerful organizing principles in mathematics, science, art, and nature. Analyzing symmetry develops spatial reasoning and prepares students for abstract algebra concepts like groups and invariance, while also having direct applications in crystallography, architecture, and design.

  • Identify all lines of symmetry in a figure and describe each as a reflection
  • Determine the order and angle of rotational symmetry of a figure
  • Classify figures as having point symmetry, line symmetry, both, or neither
  • Draw all lines of symmetry for regular polygons and explain the pattern
  • Relate the number of symmetry lines in a regular polygon to its number of sides

How to Solve: Worked Example

Example Problem: A regular octagon has rotational symmetry of what order, and what angle?
Solution Steps:
  1. The order equals the number of sides: 8.
  2. The angle of rotation is 360/8.
  3. = 45°.
Answer: order 8, 45°
Tip: Order counts how many positions look identical during one full turn — including the starting position.
1
A regular nonagon has rotational symmetry of what order, and what is its angle of rotation?
2
A regular 20-gon has rotational symmetry of what order, and what is its angle of rotation?
3
A square has rotational symmetry of what order, and what is its angle of rotation?
4
A regular 15-gon has rotational symmetry of what order, and what is its angle of rotation?
5
A regular heptagon has rotational symmetry of what order, and what is its angle of rotation?
6
A regular 30-gon has rotational symmetry of what order, and what is its angle of rotation?
7
A regular 24-gon has rotational symmetry of what order, and what is its angle of rotation?
8
A regular dodecagon has rotational symmetry of what order, and what is its angle of rotation?
9
A regular 36-gon has rotational symmetry of what order, and what is its angle of rotation?
10
An equilateral triangle has rotational symmetry of what order, and what is its angle of rotation?
11
A regular hexagon has rotational symmetry of what order, and what is its angle of rotation?
12
A regular decagon has rotational symmetry of what order, and what is its angle of rotation?
13
A regular octagon has rotational symmetry of what order, and what is its angle of rotation?
14
A regular 11-gon has rotational symmetry of what order, and what is its angle of rotation?
15
A regular 18-gon has rotational symmetry of what order, and what is its angle of rotation?
16
A regular pentagon has rotational symmetry of what order, and what is its angle of rotation?
17
A regular nonagon has rotational symmetry of what order, and what is its angle of rotation?
18
A regular 20-gon has rotational symmetry of what order, and what is its angle of rotation?
19
A square has rotational symmetry of what order, and what is its angle of rotation?
20
A regular 15-gon has rotational symmetry of what order, and what is its angle of rotation?
21
A regular heptagon has rotational symmetry of what order, and what is its angle of rotation?
22
A regular 30-gon has rotational symmetry of what order, and what is its angle of rotation?
23
A regular 24-gon has rotational symmetry of what order, and what is its angle of rotation?
24
A regular dodecagon has rotational symmetry of what order, and what is its angle of rotation?
25
A regular 36-gon has rotational symmetry of what order, and what is its angle of rotation?
26
An equilateral triangle has rotational symmetry of what order, and what is its angle of rotation?
27
A regular hexagon has rotational symmetry of what order, and what is its angle of rotation?

Answer Key

1. order 9, 40°2. order 20, 18°3. order 4, 90°4. order 15, 24°5. order 7, 51.42857142857143°6. order 30, 12°7. order 24, 15°8. order 12, 30°9. order 36, 10°10. order 3, 120°11. order 6, 60°12. order 10, 36°13. order 8, 45°14. order 11, 32.72727272727273°15. order 18, 20°16. order 5, 72°17. order 9, 40°18. order 20, 18°19. order 4, 90°20. order 15, 24°21. order 7, 51.42857142857143°22. order 30, 12°23. order 24, 15°24. order 12, 30°25. order 36, 10°26. order 3, 120°27. order 6, 60°

Frequently Asked Questions

How do I download this symmetry - worksheet 9 worksheet?

Click the "Download PDF / Print" button at the top of the worksheet. You can save it as a PDF or print it directly. The answer key will be on a separate page.

How do I find worksheets at different difficulty levels?

Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

What skills does this transformations worksheet cover?

This worksheet focuses on transformations, symmetry, geometry. It is designed for 10th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 27 problems. It typically takes 15-20 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.