IGCSE Symmetry: Complete Guide for Cambridge IGCSE Mathematics

IGCSE symmetry is an essential geometry topic in Cambridge IGCSE Mathematics that appears in both Paper 2 and Paper 4. Mastering line symmetry, rotational symmetry, and order of symmetry is essential for understanding geometric properties of shapes.

This comprehensive IGCSE symmetry guide covers everything you need to know, including identifying lines of symmetry, finding order of rotational symmetry, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to identify lines of symmetry, find order of rotational symmetry, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Geometry practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Symmetry Matters

IGCSE symmetry is an essential geometry topic. Here’s why it’s so important:

• High frequency topic: Symmetry questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for understanding geometric properties
• Exam weight: Typically worth 3-6 marks per paper
• Real-world applications: Used in design, art, and architecture
• Problem-solving skills: Develops visual and spatial reasoning

Key insight from examiners: Students often confuse line symmetry and rotational symmetry or miscount the order. This guide will help you master these systematically.

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Understanding Symmetry

Symmetry describes when a shape looks the same after a transformation.

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Line Symmetry (Reflection Symmetry)

A shape has line symmetry if it can be folded along a line so both halves match exactly.

Number of lines of symmetry = how many different lines you can fold along

Example 1: How many lines of symmetry does a square have?

Solution: A square has 4 lines of symmetry (2 diagonals + 2 through midpoints of opposite sides)

Answer: 4

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Rotational Symmetry

A shape has rotational symmetry if it looks the same after rotation.

Order of rotational symmetry = number of times the shape matches itself in a full 360° turn

Example 2: Find the order of rotational symmetry of a regular hexagon.

Solution: A regular hexagon matches itself 6 times in a full turn (every 60°)

Answer: Order 6

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Angle of Rotation

Angle of rotation = 360° / (order of rotational symmetry)

Example 3: A shape has order 4 rotational symmetry. Find the angle of rotation.

Solution: Angle = 360° / 4 = 90°

Answer: 90°

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Common Shapes and Their Symmetry

Square:

• Lines of symmetry: 4
• Rotational symmetry: Order 4

Rectangle:

• Lines of symmetry: 2
• Rotational symmetry: Order 2

Regular pentagon:

• Lines of symmetry: 5
• Rotational symmetry: Order 5

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Common Examiner Traps

• Confusing line and rotational symmetry - Line: folding; Rotational: turning
• Counting errors - Count carefully, including all lines/positions
• Regular vs irregular - Regular shapes have equal symmetry in all directions

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Practice Questions

Question 1

How many lines of symmetry does an equilateral triangle have?

Solution: An equilateral triangle has 3 lines of symmetry (one through each vertex to the midpoint of the opposite side)

Answer: 3

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Frequently Asked Questions About IGCSE Symmetry

What is line symmetry?

Line symmetry (reflection symmetry) means a shape can be folded along a line so both halves match exactly.

What is rotational symmetry?

Rotational symmetry means a shape looks the same after rotation. The order is how many times it matches in a full turn.

How do I find the order of rotational symmetry?

Count how many times the shape looks the same when rotated through 360°.

What is the angle of rotation?

Angle of rotation = 360° / (order of rotational symmetry).

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Polygons: Complete Guide - Master polygon properties
• IGCSE Transformations: Complete Guide - Master transformations
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Symmetry with Tutopiya

Ready to excel in IGCSE symmetry? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
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Book a free IGCSE maths trial lesson and get personalized support to master symmetry and achieve your target grade.

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