Class 6 ยท Maths ยท Ganita Prakash
Chapter 9 ๐ฆ
Chapter 9 ๐ฆ
Symmetry
Quick, colourful revision notes โ easy to read before your test!
Chapter Contents
What is Symmetry?
Symmetry means a part (or parts) of a figure repeat in a definite pattern โ like a flower, butterfly, rangoli or pinwheel. A shape like a cloud, with no repeating pattern, is not symmetrical.
9.1 Line of Symmetry
A line of symmetry is a line that divides a figure into two parts that exactly overlap when folded along it โ the two halves are "mirror halves".
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Fig 1: Different shapes can have different numbers of symmetry lines
A figure can have zero, one, or many lines of symmetry. A circle has infinite lines of symmetry (any line through its centre works)!
A square's diagonal is a line of symmetry โ but for a non-square rectangle, the diagonal is not a line of symmetry (try folding one to check)!
Reflection
When a figure is folded along its line of symmetry, each point on one side lands exactly on a matching point on the other side โ this is called reflection. A figure with a line of symmetry is said to have reflection symmetry.
In square ABCD, reflecting along the vertical line of symmetry swaps AโB and DโC.
9.2 Rotational Symmetry
A figure has rotational symmetry if, after rotating it by some angle (less than a full 360ยฐ turn) about a fixed point (the centre of rotation), it looks exactly the same as before.
Such an angle is called an angle of symmetry.
Such an angle is called an angle of symmetry.
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Fig 2: A square looks identical after every 90ยฐ turn โ it has 4 angles of symmetry
360ยฐ is always an angle of symmetry for every figure (a full turn always returns to the start). A square has angles of symmetry: 90ยฐ, 180ยฐ, 270ยฐ, 360ยฐ.
A figure with radial arms spaced evenly can have exactly 2, 3, 4, or more angles of symmetry โ it depends on how many arms and how evenly they're spaced!
๐ฏ Quick Summary
- Symmetry = parts of a figure repeating in a definite pattern.
- Line of symmetry = a fold line where both halves match exactly (mirror halves).
- A shape can have 0, 1, or many lines of symmetry (a circle has infinite).
- Folding along a line of symmetry = reflection โ points swap to matching positions.
- Rotational symmetry = looks the same after rotating less than 360ยฐ about a centre point.
- 360ยฐ is always an angle of symmetry for any shape; a square also has 90ยฐ, 180ยฐ, 270ยฐ.
โ๏ธ Notes by @edugrown โ happy revising! ๐