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JAC • Class 6 • Mathematics • Ch 15

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Symmetry

In JAC Board Class 6 Mathematics, "Symmetry" explores reflective balance: lines of symmetry in geometric figures (rectangles, squares, regular polygons, circles) and capital alphabet letters, and mirror reflection symmetry.

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Overview Core Concepts Formulas & Identities Solved Examples Common Traps Summary Self Check Take MCQ Test

🦋 Have You Ever Wondered?

Why do butterflies, human faces, and the Taj Mahal evoke such striking visual beauty?

Symmetry is nature's fundamental aesthetic and architectural law! Discover line symmetry and reflective balance.

Why This Chapter Matters

Before You Begin (Prerequisites)

Basic geometric shapes
Mirror reflection concept

What You Will Learn (Core Objectives)

Identify symmetrical figures and draw lines of symmetry (axis of symmetry).
Determine the number of lines of symmetry for regular polygons ($n$ lines for $n$-gon).
Identify lines of symmetry in English alphabet letters.
Understand mirror reflection symmetry and lateral inversion.

Chapter Roadmap & Progression

1 Syllabus and book alignment

2 1. Line of Symmetry

3 2. Symmetry in Shapes & Letters

Complete Concept Guide (100% Curriculum Coverage)

Syllabus and book alignment

JCERT 2026–27: Regular schools (Non-SOE) — Chapter 15 · Symmetry. Syllabus pages 228–235. These notes follow this topic. Official syllabus. Official JCERT Hindi textbook. Some source PDFs are damaged. The supplementary reference uses different chapter numbering.

1. Line of Symmetry

A figure has line symmetry if a straight line can divide it into two identical halves that fold over each other to coincide perfectly. The line is called the axis or line of symmetry.

2. Symmetry in Shapes & Letters

Line segment: 2 lines of symmetry (perpendicular bisector and line along segment).
Equilateral Triangle: 3 lines of symmetry.
Isosceles Triangle: 1 line of symmetry.
Scalene Triangle: 0 lines of symmetry.
Rectangle: 2 lines of symmetry (joining midpoints of opposite sides; NOT diagonals!).
Square: 4 lines of symmetry (2 midpoints + 2 diagonals).
Regular Polygon with $n$ sides: Exactly $n$ lines of symmetry (Hexagon = 6, Octagon = 8).
Circle: Infinitely many lines of symmetry (every diameter is a line of symmetry).
Letters: A, M, T, V, W, Y have 1 vertical line; B, C, D, E, K have 1 horizontal line; H, I, X have both horizontal and vertical lines; F, G, J, L, P, Q, R, S, Z have 0 lines of symmetry.

Key Formulas, Identities & Theorems

Regular Polygon Symmetry Rule

$$N_{\text{lines of symmetry}} = n \quad (\text{for regular } n\text{-gon})$$

Square=4, Regular Hexagon=6.

Conceptual Solved Examples & Case Studies

Example 1

How many lines of symmetry does a rectangle have? Are its diagonals lines of symmetry?

Step-by-Step Solution:

A rectangle has 2 lines of symmetry (the perpendicular bisectors of its opposite sides). Its diagonals are NOT lines of symmetry because folding along a diagonal does not make the two halves coincide.

Common Misconceptions & Examiner Traps

Common Misconception

Believing the diagonal of a rectangle is a line of symmetry.

Scientific Reality & Correction

Folding a rectangle along its diagonal results in mismatched protruding corners; only in a square do diagonals form lines of symmetry.

Visual Learning & Conceptual Map

Lines of Symmetry in Regular Polygons

An n-sided regular polygon has exactly n lines of symmetry

Equilateral Δ

3 Lines

Square

4 Lines

Reg. Pentagon

5 Lines

Circle

Infinite

Chapter Summary & 10 Key Takeaways

Takeaway 1

A line of symmetry folds a figure into two coinciding halves.

Takeaway 2

Regular n-sided polygon has n lines of symmetry.

Takeaway 3

Rectangles have 2 lines of symmetry; squares have 4; circles have infinite.

Check Your Understanding (Diagnostic Practice Questions)

Diagnostic questions testing core conceptual clarity. Answers are hidden initially — solve each problem first, then click to reveal the step-by-step verified solution.

Name a triangle with exactly one line of symmetry.

Reveal Answer & Explanation

Answer: An Isosceles triangle.
Has two equal sides.

Chapter practice

CBT tests for this chapter are not published yet. Solve the self-check questions above and compare your answers.

All Class 6 Mathematics Chapters

Ch 1: Knowing Our Numbers Ch 2: Whole Numbers Ch 3: Integers Ch 4: Playing with Numbers Ch 5: Fractions Ch 6: Decimals Ch 7: Ratio and Proportion Ch 8: Algebra Ch 9: Line, Line Segment and Ray Ch 10: Pairs of Lines Ch 11: Angles Ch 12: Polygons Ch 13: Circle Ch 14: Three-Dimensional Shapes Ch 15: Symmetry Ch 16: Practical Geometry Ch 17: Perimeter and Area Ch 18: Data Handling

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