Lines of symmetry of regular polygons: Class 6 practice
A line of symmetry divides a shape into two mirror halves. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Polygons
The idea behind lines of symmetry of regular polygons
A line of symmetry divides a shape into two mirror halves. A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.
Step-by-step method
- Identify whether the polygon is regular.
- Regular n-gon → n lines of symmetry.
- Order of rotational symmetry = n; smallest angle = 360°/n.
Worked example 1 (Basic)
How many lines of symmetry does a regular 5-sided polygon have?
- Regular 5-gon → 5 lines
- Answer: 5
Worked example 2 (Standard)
How many lines of symmetry does a regular 12-sided polygon have, and what is its order of rotational symmetry?
- Regular 12-gon → 12 lines
- Order 12
- Answer: 12 lines, order 12
Worked example 3 (Challenge)
What is the smallest angle of rotational symmetry of a regular 6-sided polygon?
- 360° ÷ 6
- = 60°
- Answer: 60°
Common mistakes and misconceptions
- Counting only vertical/horizontal lines
- Confusing order with angle
Practice questions
- (Basic) How many lines of symmetry does a regular 9-sided polygon have?
- (Basic) How many lines of symmetry does a regular 3-sided polygon have?
- (Standard) How many lines of symmetry does a regular 4-sided polygon have, and what is its order of rotational symmetry?
- (Standard) How many lines of symmetry does a regular 8-sided polygon have, and what is its order of rotational symmetry?
- (Challenge) What is the smallest angle of rotational symmetry of a regular 5-sided polygon?
- (Challenge) What is the smallest angle of rotational symmetry of a regular 10-sided polygon?
Answer key with full working
- Q1: Regular 9-gon → 9 lines → Answer: 9
- Q2: Regular 3-gon → 3 lines → Answer: 3
- Q3: Regular 4-gon → 4 lines → Order 4 → Answer: 4 lines, order 4
- Q4: Regular 8-gon → 8 lines → Order 8 → Answer: 8 lines, order 8
- Q5: 360° ÷ 5 → = 72° → Answer: 72°
- Q6: 360° ÷ 10 → = 36° → Answer: 36°
Syllabus note
This skill is listed under "Symmetry" for Class 6 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is lines of symmetry of regular polygons in?
"Symmetry", Class 6 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.