Chapter 15 of 17

88%

Tamil Nadu (TNBSE)Class 7 Mathematics★ 5-9 marks in the TN Class 7 Term 3 exam through symmetry and construction questions

Geometry (Term 3) - Symmetry and Constructions

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 3 Chapter 4, Geometry. Reflection (mirror) symmetry and lines of symmetry, rotational and translational symmetry, concentric circles, and the construction of circles, with worked examples, exercises and quick revision.

⏱ 14 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
2Find the order of rotational symmetry
3Recognise translational symmetry
4Describe concentric circles
5Construct circles of a given radius

💡

Why this chapter matters

Symmetry and constructions appear in art, design and nature and develop spatial reasoning. Lines of symmetry, rotational symmetry and circle construction are directly tested in the TN Class 7 Term 3 exam.

Before you start — revise these

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

🔗

Term 2 — Geometry (Triangles)

Shapes and figures.

Geometry (Symmetry and Constructions) — Class 7 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 7 Mathematics, Term 3 — Chapter 4. Symmetry, transformations and circle constructions.

1. About this chapter

This chapter covers reflection (mirror) symmetry, rotational and translational symmetry, concentric circles, and the construction of circles.

2. Reflection (line) symmetry

A figure has line (reflection) symmetry if a line (the line of symmetry / mirror line) divides it into two mirror-image halves.
Examples: a square has 4 lines of symmetry, a rectangle 2, an equilateral triangle 3, a circle infinitely many.

3. Rotational and translational 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).
Translational symmetry is when a pattern repeats by sliding (translating) a fixed distance — as in borders and wallpaper.

4. Circles and constructions

Concentric circles share the same centre but have different radii.
To construct a circle, open the compass to the radius, place the point at the centre and draw the full circle. A circle of a given radius is drawn from a marked centre.

5. Worked examples

Example 1. How many lines of symmetry does a rectangle have? Two (through the midpoints of opposite sides).

Example 2. What is the order of rotational symmetry of an equilateral triangle? 3 (it matches three times in a full turn).

Example 3. What are concentric circles? Circles with the same centre but different radii.

6. Exercises (Samacheer Kalvi)

Draw all the lines of symmetry of a square.
State the number of lines of symmetry: (a) circle (b) equilateral triangle (c) letter H.
Find the order of rotational symmetry of a square.
Draw two concentric circles of radii 2 cm and 3.5 cm.
Construct a circle of radius 4 cm.

7. Common mistakes

Mistake: Confusing line symmetry with rotational symmetry. Fix: Line symmetry = mirror halves; rotational symmetry = looks the same after turning.
Mistake: Saying a rectangle has 4 lines of symmetry. Fix: A rectangle has only 2 (a square has 4).
Mistake: Thinking concentric circles can have different centres. Fix: Concentric circles share the same centre.

8. Quick revision

Term 3 · Ch 4 · symmetry and constructions.
Line symmetry: mirror halves (square 4, rectangle 2, equilateral triangle 3, circle infinite).
Rotational symmetry: matches on turning; order = number of matches in a full turn.
Translational symmetry: repeating by sliding. Concentric circles share a centre; construct circles with a compass set to the radius.

Key formulas & results

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

Line symmetry

mirror line splits into equal halves

Square 4, rectangle 2.

Rotational symmetry

order = matches in one full turn

Square order 4.

Translational symmetry

pattern repeats by sliding

Borders, wallpaper.

Concentric circles

same centre, different radii

Compass construction.

⚠️

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

✗ Saying a rectangle has 4 lines of symmetry

✓ A rectangle has only 2 (a square has 4).

WATCH OUT

✗ Thinking concentric circles can have different centres

✓ Concentric circles share the same centre.

NCERT exercises (with solutions)

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

Lines of symmetry

Find lines of symmetry of shapes and letters.

Questions

Rotational symmetry

Find the order of rotational symmetry.

Questions

Constructions

Draw circles and concentric circles.

Questions

Practice problems

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

Q1EASY· Line symmetry

How many lines of symmetry does a rectangle have?

▶ Show solution

Two.

Q2EASY· Line symmetry

How many lines of symmetry does a circle have?

▶ Show solution

Infinitely many.

Q3EASY· Rotational

What is the order of rotational symmetry of an equilateral triangle?

▶ Show solution

3.

Q4EASY· Concept

What are concentric circles?

▶ Show solution

Circles with the same centre but different radii.

Q5MEDIUM· Line symmetry

State the number of lines of symmetry of a square and the letter H.

▶ Show solution

Square: 4; letter H: 2.

Q6EASY· Construction

How do you construct a circle of radius 4 cm?

▶ Show solution

Open the compass to 4 cm, place the point at the chosen centre and draw the full circle.

5-minute revision

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

•Term 3 Chapter 4 of Samacheer Kalvi Class 7 Maths.
•Line (reflection) symmetry: a mirror line splits a figure into equal halves.
•Square 4, rectangle 2, equilateral triangle 3, circle infinite 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.
•Concentric circles share a centre; construct a circle with a compass set to the radius.

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 and constructions

Question type	Marks each	Typical count	What it tests
Line symmetry	1-2	2-3	Counting lines of symmetry
Rotational symmetry	1-2	1	Order of symmetry
Construction	2	1	Drawing circles

Prep strategy

Fold or imagine mirror lines to count symmetry
Turn the shape to find rotational order
Remember square 4, rectangle 2 lines
Practise compass constructions

Where this shows up in the real world

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

Art and design

Rangoli, logos and patterns use symmetry.

Nature

Flowers, leaves and snowflakes show symmetry.

Engineering

Symmetric parts balance machines and structures.

Exam strategy

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

Count lines of symmetry by imagining folds
Rotate mentally to find the order
State exact counts (square 4, rectangle 2)
Show compass arcs in constructions

Going beyond the textbook

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

Find all capital letters of the alphabet with exactly two lines of symmetry.
Design a border pattern with translational symmetry.

Where else this chapter is tested

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

TN Class 7 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.

Line symmetry means a mirror line divides a figure into matching halves; rotational symmetry means the figure looks unchanged after being turned by less than a full circle about its centre.

It is the number of times a figure looks exactly the same during one complete 360° turn — for example, a square matches 4 times, so its order is 4.

Practice more, ask doubts, find a tutor

Tamil Nadu (TNBSE) Class 7 mock tests

Tamil Nadu (TNBSE) Class 7 PYQs

Ask in Q&A

Mathematics flashcards

Related chapters

Students who read Geometry (Term 3) - Symmetry and Constructions usually read these next.

Number System (Term 1) - Integers

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 1 Chapter 1, Number System. Integers on the number line, the four fundamental operations on integers, and their properties — closure, commutative, associative, distributive, identity — with the rules of signs in multiplication and division, worked examples, exercises and quick revision.

Measurements (Term 1) - Area and Perimeter

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 1 Chapter 2, Measurements. The concepts of perimeter and area and the formulae for the area and perimeter of a parallelogram, a rhombus and a trapezium, with their properties, worked examples, exercises and quick revision.

Algebra (Term 1) - Expressions and Equations

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 1 Chapter 3, Algebra. Algebraic expressions and their terms, factors and coefficients, like and unlike terms, addition and subtraction of expressions, evaluating expressions, and solving simple linear equations and word problems, with worked examples, exercises and quick revision.

Direct and Inverse Proportion

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 1 Chapter 4, Direct and Inverse Proportion. Ratio and proportion, direct proportion (quantities rise and fall together) and inverse proportion (one rises as the other falls), and the unitary method, with worked examples, exercises and quick revision.

🧑‍🏫