Symmetry - Worksheet 3 - 10th Grade

Easy

Identify line and rotational symmetry in figures (Easy)

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

About This Worksheet

This easy-level worksheet contains 18 problems designed for 10th Grade students practicing line & rotational symmetry. Easy worksheets use simpler numbers and straightforward problem types to build confidence and reinforce foundational skills.

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: How many lines of symmetry does a regular decagon have?
Solution Steps:
  1. A regular n-gon has exactly n lines of symmetry.
  2. A decagon has 10 sides.
  3. So it has 10 lines of symmetry.
Answer: 10
Tip: For an even-sided regular polygon, half the lines pass through vertices and half through edge midpoints.
1
How many lines of symmetry does a regular decagon have?
2
How many lines of symmetry does a regular 15-gon have?
3
How many lines of symmetry does a regular nonagon have?
4
How many lines of symmetry does a regular heptagon have?
5
How many lines of symmetry does a regular 11-gon have?
6
How many lines of symmetry does a equilateral triangle have?
7
How many lines of symmetry does a regular 36-gon have?
8
How many lines of symmetry does a regular 18-gon have?
9
How many lines of symmetry does a regular 24-gon have?
10
How many lines of symmetry does a regular dodecagon have?
11
How many lines of symmetry does a regular pentagon have?
12
How many lines of symmetry does a regular octagon have?
13
How many lines of symmetry does a regular hexagon have?
14
How many lines of symmetry does a regular 20-gon have?
15
How many lines of symmetry does a square have?
16
How many lines of symmetry does a regular 30-gon have?
17
How many lines of symmetry does a regular decagon have?
18
How many lines of symmetry does a regular 15-gon have?

Answer Key

1. 102. 153. 94. 75. 116. 37. 368. 189. 2410. 1211. 512. 813. 614. 2015. 416. 3017. 1018. 15

Frequently Asked Questions

How do I download this symmetry - worksheet 3 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 18 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.