Summary
Chapter 9 of the Class 6 Maths NCERT textbook (Ganita Prakash), "Symmetry", covers line of symmetry (reflection symmetry) and rotational symmetry — teaching students to identify, draw, and reason about symmetric figures through folding, cutting, and rotation activities.
- Reflection (line) symmetry — A line of symmetry folds a figure into two mirror halves that overlap exactly. A figure can have several such lines — a square has 4 and an equilateral triangle has 3 — while a triangle never has exactly 2.
- Rotational symmetry — A figure has rotational symmetry when it looks unchanged after a turn strictly between 0° and 360° about a fixed centre. 360° always works, and every angle of symmetry is a multiple of the smallest one.
- Symmetry of special figures — A regular polygon with n sides has n lines and n angles of symmetry, while a circle has infinitely many of each. The Ashoka Chakra shows 24 lines and 24 angles, with a smallest angle of 15°.
Key points & formulas
- 01A line of symmetry (axis of symmetry) divides a figure into two mirror halves that exactly overlap when folded.
- 02A figure may have multiple lines of symmetry — a square has 4 (2 along midpoints, 2 along diagonals); an equilateral triangle has 3.
- 03The diagonal of a rectangle that is NOT a square is not a line of symmetry.
- 04A figure with a line (or lines) of symmetry is said to have reflection symmetry.
- 05Rotational symmetry exists when a figure looks the same after rotating by some angle strictly between 0° and 360° about a fixed centre of rotation.
- 06360° is always an angle of rotational symmetry for every figure.
- 07All angles of symmetry of a figure are multiples of the smallest angle of symmetry.
- 08If the smallest angle of symmetry is a natural number in degrees, it must be a factor of 360.
- 09A circle has infinitely many lines of symmetry (every diameter) and every angle is an angle of symmetry.
- 10A regular polygon with n sides has n lines of symmetry and n angles of rotational symmetry.
- 11The Ashoka Chakra has 24 lines of symmetry and 24 angles of symmetry (smallest = 15°).
- 12A triangle can have 0, 1, or 3 lines of symmetry — never exactly 2.
Frequently asked questions
01What is Chapter 9 Symmetry in Class 6 Maths (Ganita Prakash) about?
Chapter 9 teaches two types of symmetry: line (reflection) symmetry, where a figure folds into two identical mirror halves, and rotational symmetry, where a figure looks the same after being rotated by a certain angle about a fixed centre. Students explore these through hands-on activities like folding, cutting, and paper rotation.
02What is a line of symmetry?
A line that cuts a figure into two parts that exactly overlap when folded along that line is called a line of symmetry (or axis of symmetry). The two halves are called mirror halves.
03How many lines of symmetry does a square have?
A square has 4 lines of symmetry: one vertical (through midpoints of top and bottom sides), one horizontal (through midpoints of left and right sides), and two diagonal (one along each diagonal).
04Is the diagonal of a rectangle a line of symmetry?
Only if the rectangle is a square. For a rectangle that is not a square, the diagonal is NOT a line of symmetry — folding along the diagonal does not produce two overlapping halves.
05What is rotational symmetry?
A figure has rotational symmetry when it looks exactly the same after being rotated by some angle strictly between 0° and 360° about a fixed point called the centre of rotation. The angle at which it repeats is called the angle of rotational symmetry.
06Why is 360° always an angle of symmetry for every figure?
When any figure is rotated by 360°, it completes a full turn and returns to its exact original position. Therefore, 360° is always an angle of symmetry for every figure.
07What is the relationship between angles of symmetry?
All angles of symmetry of a figure are multiples of the smallest angle of symmetry. For example, if the smallest angle is 90°, the angles of symmetry are 90°, 180°, 270°, and 360°.
08How many angles of symmetry does a circle have?
A circle has infinitely many angles of symmetry — every possible angle is an angle of symmetry for a circle, since rotating a circle by any amount about its centre still gives the same circle.
09Can a triangle have exactly two lines of symmetry?
No. A triangle can have exactly 0 lines of symmetry (scalene), exactly 1 line (isosceles), or exactly 3 lines (equilateral). It is impossible for a triangle to have exactly 2 lines of symmetry.
10How many lines of symmetry does the Ashoka Chakra have?
The Ashoka Chakra has 24 lines of symmetry and 24 angles of rotational symmetry. Its smallest angle of rotational symmetry is 360° ÷ 24 = 15°.
11How many lines and angles of symmetry does a regular polygon with n sides have?
A regular polygon with n equal sides and n equal angles has exactly n lines of symmetry and n angles of rotational symmetry. For example: equilateral triangle (3), square (4), regular pentagon (5), regular hexagon (6).
12Is the NCERT Ganita Prakash Class 6 Chapter 9 PDF free to download with no sign-up?
Yes — the official NCERT Ganita Prakash Class 6 PDF is free to download. On this site you can access it directly with no account or sign-up required.
More chapters in Ganita Prakash
Read Chapter 9 of Ganita Prakash, the Class 6 Mathematics NCERT textbook (2026-27 edition), online for free: the complete chapter as published by NCERT with every diagram, solved example and exercise, with step-by-step solutions, answers and revision notes. Open the NCERT PDF above, or browse all NCERT Class 6 textbooks.
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