Symmetry
Overview
Symmetry is a fundamental concept in mathematics and nature. A figure has symmetry when one part mirrors another. In Class 7, we study lines of symmetry, rotational symmetry, and the relationship between them. We explore how many lines of symmetry different shapes have and how figures rotate about a centre point to look the same. Symmetry is seen in art, architecture, and everyday objects around us.
Typed Notes
Lines of Symmetry
A line of symmetry is an imaginary line that divides a shape into two equal halves that are mirror images of each other. For example, an equilateral triangle has 3 lines of symmetry, a square has 4, and a circle has infinite lines of symmetry. A scalene triangle has no line of symmetry. We can find lines of symmetry by folding a shape — if both halves match perfectly, the fold line is a line of symmetry. Regular polygons always have lines of symmetry equal to their number of sides.
Rotational Symmetry
A figure has rotational symmetry if it looks exactly the same after being rotated by a certain angle about a fixed centre point, called the centre of rotation. The angle at which this happens is the angle of rotation. For example, a square looks the same after rotating 90°, 180°, 270°, and 360°, so its order of rotational symmetry is 4. An equilateral triangle has rotational symmetry of order 3 (rotations of 120°, 240°, 360°). The angle of rotation = 360° ÷ order of rotational symmetry.
Line Symmetry and Rotational Symmetry Together
Many figures have both line symmetry and rotational symmetry. A square has 4 lines of symmetry and rotational symmetry of order 4. An equilateral triangle has 3 lines of symmetry and rotational symmetry of order 3. Some figures have only one type — a rectangle has 2 lines of symmetry and rotational symmetry of order 2. The letter S has rotational symmetry of order 2 but no line of symmetry. Understanding both types together helps us fully describe the symmetry of any figure or object.
Symmetry in Real Life and Special Figures
Symmetry appears everywhere — in snowflakes, flowers, butterflies, and buildings. A circle has infinite lines of symmetry and infinite rotational symmetry. A parallelogram has no line of symmetry but has rotational symmetry of order 2. An arrow pointing right has one line of symmetry (horizontal). Recognising symmetry helps in art, design, and problem solving. When a figure has rotational symmetry of order n, the angle of rotation is 360°/n. Figures like the recycling symbol have rotational symmetry of order 3 with no line of symmetry.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01A line of symmetry divides a figure into two identical mirror-image halves.
- 02Regular polygons have lines of symmetry equal to the number of their sides.
- 03Rotational symmetry exists when a figure looks the same after being rotated by less than 360°.
- 04The order of rotational symmetry is the number of times a figure looks the same in one full rotation of 360°.
- 05Every figure has rotational symmetry of order 1 (at 360°), but we say it has no rotational symmetry if order is 1.
Important Formulas
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
How many lines of symmetry does a regular hexagon have? Also find its order of rotational symmetry and angle of rotation.
A figure has rotational symmetry of order 4. What is its angle of rotation? Name a shape with this property.
Does a rectangle have line symmetry? If yes, how many lines? Does it have rotational symmetry and what is its order?
An equilateral triangle has rotational symmetry. At what angles does it look the same? What is the order?
A regular pentagon has 5 sides. Find its number of lines of symmetry, order of rotational symmetry, and angle of rotation.
Symmetry involves lines of symmetry that create mirror-image halves and rotational symmetry where figures look the same after rotation. Regular polygons have lines of symmetry equal to their sides. Order of rotational symmetry tells how many times a figure matches itself in 360°. Angle of rotation equals 360° divided by the order. Many shapes possess both types of symmetry simultaneously.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.How many lines of symmetry does a square have?
Q2.What is the order of rotational symmetry of an equilateral triangle?
Q3.A figure has an angle of rotation of 90°. What is its order of rotational symmetry?
Q4.Which of the following has NO line of symmetry?
Mark karo — dashboard par progress dikhega.