Complete Summary, Explanations, and Solutions for Symmetry – Ganita Prakash Class VI, Chapter 9 – Line Symmetry, Rotational Symmetry, Reflection, Questions, Answers
Detailed summary and explanation of Chapter 9 'Symmetry' from the Ganita Prakash Mathematics textbook for Class VI, covering line of symmetry, mirror halves, reflection symmetry, multiple lines of symmetry, paper folding and cutting activities, ink blot patterns, punching game, rotational symmetry, centre of rotation, angles of symmetry, radial arms, symmetries of circle, figures with both line and rotational symmetry—along with all NCERT questions, answers, and step-by-step solutions.
Tags: Symmetry, Ganita Prakash, NCERT, Class 6, Mathematics, Geometry, Line Symmetry, Line of Symmetry, Axis of Symmetry, Mirror Halves, Reflection Symmetry, Multiple Lines of Symmetry, Paper Folding, Paper Cutting, Ink Blot, Punching Game, Rotational Symmetry, Centre of Rotation, Angles of Symmetry, Order of Rotational Symmetry, Radial Arms, Circle Symmetry, Regular Polygons, Symmetrical Figures, Summary, Explanation, Questions, Answers, Solutions, Chapter 9
This chapter explores symmetry in figures, including line symmetry and rotational symmetry, with practical activities like paper folding and cutting to understand and generate symmetrical shapes.
Main Topics Covered
Introduction to symmetry: Repeating patterns in figures like flowers, butterflies, rangoli.
Line of symmetry: Mirror halves, multiple lines in shapes like squares.
Reflection symmetry: Reflecting parts across lines.
Generating symmetrical shapes: Ink blots, paper folding/cutting, punching.
Rotational symmetry: Angles of rotation, center of rotation.
Symmetries in regular polygons, circles, and structures like Taj Mahal.
Activities: Playing with tiles, games for symmetry.
Key Takeaways for Exams
Line Symmetry
Fold to overlap halves.
Multiple Lines
Square: 4, equilateral triangle: 3.
Reflection
Mirror image across line.
Rotational Symmetry
Angles like 90°, 180°, etc.
Circle Symmetries
Infinite lines, all angles.
Radial Arms
Equal angles for symmetry.
Key Rules & Properties – Symmetry
Important rules for identifying and creating symmetry.
Line Symmetry Rules
Folding and overlapping.
Shape
Lines of Symmetry
Example
Square
4 (vertical, horizontal, diagonals)
Fold halves overlap.
Equilateral Triangle
3 (altitudes)
Mirror halves.
Rectangle (non-square)
2 (vertical, horizontal)
Diagonals not symmetric.
Regular Hexagon
6
Equal sides/angles.
Circle
Infinite (diameters)
Any diameter.
Rotational Symmetry Rules
Property
Rule
Example
Angles
Multiples of smallest angle, up to 360°
Square: 90°, 180°, 270°, 360°
Order
Number of angles (excluding 360° sometimes)
Equilateral triangle: 3 (120°, 240°, 360°)
Radial Arms
Equal angles = 360°/n
3 arms: 120° each
Circle
All angles
Infinite rotational symmetry
Smallest Angle
Must divide 360° evenly for integer orders
45°: Yes (8 times); 17°: No
Properties
Reflection Symmetry: Parts mirror across line.
Generating: Folding/cutting creates symmetry.
Combination: Some shapes have both line and rotational.
No Symmetry: Irregular figures like clouds.
Concept Cards – Quick Explanations
Symmetry Definition
Repeating parts in definite pattern.
Line of Symmetry
Fold line where halves overlap.
Mirror Halves
Identical reflected parts.
Multiple Lines
Shapes like square have 4.
Reflection Symmetry
Mirror image across line.
Ink Blot
Fold and press for symmetry.
Paper Cutting
Fold and cut for patterns.
Rotational Symmetry
Rotate to overlap original.
Center of Rotation
Fixed point for turning.
Angles of Symmetry
90°, 180°, etc., multiples.
Radial Arms
Equal angles for order n.
Circle Symmetry
Infinite lines and rotations.
Examples + Solutions
Example 1: Line Symmetry in Square
Solution: 4 lines: Vertical, horizontal, two diagonals. Fold overlaps.
Example 2: Reflection in Square
Solution: Points A to B, B to A on vertical; similar for others.
