Chapter 15 of 16

94%

Tamil Nadu (TNBSE)Class 6 Mathematics★ 5-9 marks in the TN Class 6 Term 3 exam through line and rotational symmetry questions

Symmetry

Samacheer Kalvi (TN State Board) Class 6 Maths — Term 3 Chapter 4, Symmetry. Line (reflection) symmetry and lines of symmetry of regular polygons, rotational symmetry and its order, and translational symmetry, with worked examples, exercises and quick revision.

⏱ 13 min readEasy difficulty✓ Free · NCERT-aligned

Worksheet

Podcast

Listen as a conversation

A teacher & a student talk through the chapter — in your language.

Mind Map

The chapter at a glance

Every concept and exam-favourite branch — revisable in 5 minutes.

…

Study Guide

Night-before notes

Key points, glossary and the questions most likely to show up.

…

VocabularyBuild your vocabularyLexiGenome mines the key words and schedules them with spaced repetition.Mine words →

By the end of this chapter you'll be able to…

1Identify lines of reflection symmetry
2State the lines of symmetry of regular polygons
3Find the order of rotational symmetry
4Recognise translational symmetry
5Give examples of each type

💡

Why this chapter matters

Symmetry appears in art, nature and design and develops spatial reasoning. Lines of symmetry and rotational symmetry are directly tested in the TN Class 6 Term 3 exam.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

🔗

Term 1 — Geometry (Lines and Angles)

Shapes and figures.

Symmetry — Class 6 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 6 Mathematics, Term 3 — Chapter 4. Reflection, rotation and translation.

1. About this chapter

This chapter covers line (reflection) symmetry and the lines of symmetry of regular polygons, rotational symmetry and its order, and translational symmetry.

2. Line (reflection) symmetry

A figure has line symmetry if a line (the line of symmetry / mirror line) divides it into two identical mirror-image halves.
A regular polygon of n sides has n lines of symmetry: equilateral triangle 3, square 4, regular pentagon 5, regular hexagon 6; a circle has infinitely many.

3. Rotational symmetry

A figure has rotational symmetry if it looks the same after a rotation of less than a full turn about a centre.
The order of rotational symmetry is the number of times it matches in one full turn: a square has order 4, an equilateral triangle order 3.

4. Translational symmetry

Translational symmetry is when a pattern repeats by sliding (translating) a fixed distance, as in borders, tiles and wallpaper.

5. Worked examples

Example 1. How many lines of symmetry does a regular hexagon have? 6 (one for each side).

Example 2. What is the order of rotational symmetry of a square? 4.

Example 3. Which figure has infinitely many lines of symmetry? A circle.

6. Exercises (Samacheer Kalvi)

Draw all the lines of symmetry of (a) an equilateral triangle (b) a square.
State the number of lines of symmetry of a regular pentagon.
Find the order of rotational symmetry of an equilateral triangle.
Name a shape with rotational symmetry of order 2.
Give one example of translational symmetry from daily life.

7. Common mistakes

Mistake: Confusing line symmetry with rotational symmetry. Fix: Line symmetry = mirror halves; rotational symmetry = looks the same after turning.
Mistake: Giving a regular polygon the wrong number of lines. Fix: A regular n-sided polygon has n lines of symmetry.
Mistake: Forgetting that a circle has infinite symmetry. Fix: A circle has infinitely many lines of symmetry and infinite rotational symmetry.

8. Quick revision

Term 3 · Ch 4 · symmetry.
Line symmetry: mirror halves; regular n-gon has n lines (triangle 3, square 4, hexagon 6, circle infinite).
Rotational symmetry: looks the same on turning; order = matches in a full turn.
Translational symmetry: a pattern repeats by sliding.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Line symmetry

mirror line splits into identical halves

Reflection.

Regular polygon

n-sided polygon has n lines of symmetry

Triangle 3, square 4, hexagon 6.

Rotational symmetry

order = matches in one full turn

Square order 4.

Translational symmetry

pattern repeats by sliding

Borders, tiles.

⚠️

Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Confusing line symmetry with rotational symmetry

✓ Line symmetry = mirror halves; rotational symmetry = looks the same after turning.

WATCH OUT

✗ Giving a regular polygon the wrong number of lines

✓ A regular n-sided polygon has n lines of symmetry.

WATCH OUT

✗ Forgetting that a circle has infinite symmetry

✓ A circle has infinitely many lines of symmetry.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Lines of symmetry

Draw and count lines of symmetry.

Questions

Rotational symmetry

Find the order of rotational symmetry.

Questions

Translational symmetry

Identify repeating patterns.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Line symmetry

How many lines of symmetry does a regular hexagon have?

▶ Show solution

6.

Q2EASY· Rotational

What is the order of rotational symmetry of a square?

▶ Show solution

4.

Q3EASY· Line symmetry

Which figure has infinitely many lines of symmetry?

▶ Show solution

A circle.

Q4EASY· Line symmetry

How many lines of symmetry does a regular pentagon have?

▶ Show solution

5.

Q5EASY· Rotational

Name a shape with rotational symmetry of order 3.

▶ Show solution

An equilateral triangle.

Q6MEDIUM· Concept

Give one example each of line and translational symmetry.

▶ Show solution

Line symmetry: a butterfly or the letter A; translational symmetry: a repeating border or tiled floor.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Term 3 Chapter 4 of Samacheer Kalvi Class 6 Maths.
•Line (reflection) symmetry: a mirror line gives identical halves.
•A regular n-sided polygon has n lines of symmetry (triangle 3, square 4, hexagon 6).
•A circle has infinitely many lines of symmetry.
•Rotational symmetry: a figure looks the same after a turn; order = matches in a full turn.
•Translational symmetry: a pattern repeats by sliding.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 5-9 marks across symmetry

Question type	Marks each	Typical count	What it tests
Line symmetry	1	2-3	Lines of symmetry
Rotational	1-2	1-2	Order of symmetry
Translational	2	1	Repeating patterns

Prep strategy

Use the n-sides = n-lines rule
Turn the shape to find rotational order
Remember a circle has infinite symmetry
Spot sliding patterns for translation

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Art

Rangoli and designs use symmetry.

Nature

Flowers, leaves and butterflies are symmetric.

Architecture

Buildings often use symmetry for balance.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Apply n-sides = n-lines for regular polygons
Rotate mentally to find the order
State a circle has infinite symmetry
Identify sliding patterns for translation

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

List the capital letters with rotational symmetry of order 2.
Find the order of rotational symmetry of a regular hexagon.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 6 Term 3 ExamMedium

NMMS / Foundation MathsMedium

School unit testsHigh

AI helpers for this chapter

Generate more practice on the fly, or have the chapter explained at a different level.

⚡

Generate 5 more questions

Fresh MCQs + short-answer items based on this chapter, plus answer keys.

🧠

Explain at a different level

Re-explain the chapter at the level you actually want.

📝 My notes

Saved on this device — sign in to sync · how this works

0/600

Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Exactly as many as it has sides — an equilateral triangle has 3, a square 4, a regular pentagon 5, and so on.

It is the number of times a figure looks exactly the same as you turn it through one full 360° rotation; for example, a square matches 4 times, so its order is 4.

Practice more, ask doubts, find a tutor

Tamil Nadu (TNBSE) Class 6 mock tests

Tamil Nadu (TNBSE) Class 6 PYQs

Ask in Q&A

Mathematics flashcards

Related chapters

Students who read Symmetry usually read these next.

Numbers (Term 1) - Whole Numbers

Samacheer Kalvi (TN State Board) Class 6 Maths — Term 1 Chapter 1, Numbers. Reading and writing large numbers, place value and the Indian and international systems, ascending and descending order, rounding (estimation), the properties of whole numbers and the BODMAS rule, with worked examples, exercises and quick revision.

Introduction to Algebra

Samacheer Kalvi (TN State Board) Class 6 Maths — Term 1 Chapter 2, Introduction to Algebra. Constants and variables, writing algebraic expressions, using a variable to describe patterns, and forming and solving simple linear equations from word problems, with worked examples, exercises and quick revision.

Ratio and Proportion

Samacheer Kalvi (TN State Board) Class 6 Maths — Term 1 Chapter 3, Ratio and Proportion. The meaning of a ratio, equivalent ratios and simplest form, the meaning of proportion, and the unitary method for solving everyday problems, with worked examples, exercises and quick revision.

Geometry (Term 1) - Lines and Angles

Samacheer Kalvi (TN State Board) Class 6 Maths — Term 1 Chapter 4, Geometry. Points, lines, rays and line segments, measuring angles with a protractor, the types of angles, special angles (30°, 45°, 60°, 90°, 120°) and supplementary angles, with worked examples, exercises and quick revision.

🧑‍🏫