Symmetry Class 7 Chapter Notes
Symmetry is a scoring Class 7 Maths chapter because most questions are visual, pattern-based and quick if you remember the rules. These notes cover line symmetry, rotational symmetry, order of rotation, common shapes, alphabets, and exam traps such as counting diagonals wrongly or forgetting the full turn of 360°. In CBSE exams, you may be asked to draw lines of symmetry, complete a symmetric figure, identify rotational symmetry, or compare shapes like square, rectangle, triangle and regular polygon. Revise this chapter by first memorising the common-shape table, then practising 5–10 diagrams by folding or mentally reflecting them. Use YoLearn AI Tools to turn these notes into Flashcards, create a quick Mind Map of shape properties, attempt a short Quiz, and use the Summarizer for last-minute revision before class tests.
Key points
- A figure has line symmetry if one half exactly overlaps the other half when folded along a line.
- The fold line is called the line of symmetry or axis of symmetry.
- A figure has rotational symmetry if it looks exactly the same after a turn less than 360° about a fixed point.
- The fixed point used for turning is the centre of rotation.
- Order of rotational symmetry = number of times a figure matches itself in one complete turn of 360°.
- For a regular polygon with n equal sides, number of lines of symmetry = n and order of rotational symmetry = n.
- Angle for the next matching position of a regular n-sided polygon = 360° ÷ n.
- A rectangle has 2 lines of symmetry and rotational symmetry of order 2; a square has 4 lines of symmetry and rotational symmetry of order 4.
- Do not assume every diagonal is a line of symmetry. Diagonals of a square are lines of symmetry, but diagonals of a rectangle are not.
- A shape with no visible mirror line may still have rotational symmetry, for example some pinwheel-like designs.
Important definitions
- Symmetry
- A property of a figure in which parts of the figure match exactly in size, shape and position after folding, reflection or rotation.
- Line symmetry
- A figure has line symmetry when it can be divided by a line into two identical mirror-image halves.
- Line of symmetry
- The imaginary fold line that divides a figure into two exactly matching halves.
- Reflection
- A mirror-like flipping of a figure across a line, where each point has a matching point at the same distance on the other side.
- Rotational symmetry
- A figure has rotational symmetry if it coincides with itself after rotation through an angle less than 360° about a fixed point.
- Centre of rotation
- The fixed point around which a figure is rotated while checking rotational symmetry.
- Angle of rotation
- The angle through which a figure is turned about its centre to reach a new position.
- Order of rotation
- The number of times a figure looks exactly the same during one complete 360° rotation.
- Regular polygon
- A polygon with all sides equal and all angles equal, such as an equilateral triangle, square or regular pentagon.
Core idea: why symmetry means exact matching
In Class 7, symmetry means exact matching, not just looking similar. For line symmetry, imagine folding a paper shape along a possible line. If the left half covers the right half exactly, that line is a line of symmetry. The matching parts must have the same size and shape, and they must lie at equal distances from the fold line. For rotational symmetry, imagine placing a pin at the centre of the figure and turning it. If the figure looks exactly the same before completing a full 360° turn, it has rotational symmetry. The number of matching positions in one full turn gives the order of rotation. A square is useful to remember: it matches at 90°, 180°, 270° and 360°, so its order is 4. A general irregular shape usually has no line symmetry and only order 1 rotational symmetry, because it matches only after the full 360° turn.
Line symmetry vs rotational symmetry
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How to test symmetry in exam diagrams
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Common shapes: quick revision table
Worked mini-examples
- {"title":"Example 1: Count lines of symmetry of a rectangle","bodyMarkdown":"A rectangle has two pairs of equal opposite sides. It can be folded exactly through the middle vertically and horizontally. Its diagonals do not divide it into mirror-image halves. Answer: 2 lines of symmetry."}
- {"title":"Example 2: Find order of rotation of a square","bodyMarkdown":"A square looks the same after turns of 90°, 180°, 270° and 360° about its centre. Hence it coincides 4 times in one complete turn. Answer: order = 4; smallest angle = 360° ÷ 4 = 90°."}
- {"title":"Example 3: Regular hexagon angle of rotation","bodyMarkdown":"A regular hexagon has 6 equal sides and 6 equal angles. It matches itself 6 times in 360°. Order = 6; smallest angle of rotation = 360° ÷ 6 = 60°."}
Regular polygons shortcut
A regular polygon is the easiest type of figure for symmetry questions because all its sides and angles are equal. For a regular polygon with n sides, it has n lines of symmetry and rotational symmetry of order n. This means a regular triangle has 3, a square has 4, a regular pentagon has 5, and a regular hexagon has 6. The smallest angle through which it must be turned to look the same again is 360°/n. This shortcut works only for regular polygons. Do not apply it to irregular pentagons or ordinary quadrilaterals because their sides and angles may not match.
Exam tip: common CBSE marking traps
When asked to draw lines of symmetry, use a ruler and make the line pass through the exact centre or correct vertices. In rotational symmetry questions, do not write only the angle; also write the order if asked. Remember: a shape with rotational symmetry of order 1 is usually treated as having no non-trivial rotational symmetry because it matches only after 360°. For regular polygons, show the formula 360° ÷ n when finding the smallest angle; this helps secure method marks.
Quick revision checks
- Q: How many lines of symmetry does a square have? A: 4 lines of symmetry: vertical, horizontal and two diagonals.
- Q: What is the order of rotational symmetry of a rectangle? A: 2, because it matches at 180° and 360°.
- Q: What is the smallest angle of rotation of a regular pentagon? A: 360° ÷ 5 = 72°.
- Q: Does every triangle have a line of symmetry? A: No. An equilateral triangle has 3, an isosceles triangle has 1, and a scalene triangle has none.
Frequently Asked Questions
What is symmetry in Class 7 Maths?
Symmetry means exact matching of parts of a figure. In Class 7, you mainly study line symmetry, where halves match after folding, and rotational symmetry, where a figure matches itself after turning.
How do I find the number of lines of symmetry?
Imagine folding the figure along possible vertical, horizontal and diagonal lines. Count only those lines where both parts overlap exactly, not just lines that divide the area into two parts.
What is order of rotational symmetry?
Order of rotational symmetry is the number of times a figure coincides with itself in one complete 360° turn. For example, a square has order 4 and a rectangle has order 2.
What is the formula for the smallest angle of rotation?
For a regular polygon, smallest angle of rotation = 360° ÷ number of sides. Example: for a regular hexagon, 360° ÷ 6 = 60°.
Can a figure have rotational symmetry but no line symmetry?
Yes. Some designs look the same after rotation but cannot be folded into mirror-image halves. Always test folding and turning separately.