## Class 6 Maths Chapter 9 Symmetry Notes

**Class 6 Maths Chapter 9 Notes – Class 6 Symmetry Notes**

→ There are many figures or objects which when folded along a straight line are divided equally into two identical halves such that one part coincides with the other. Such figures are called symmetrical figures.

→ The line which divides a symmetrical figure into two equal parts that exactly overlaps when folded along that line is called line of symmetry. The idea of symmetry is used in almost all activities of our day-to-day life.

→ The concept of symmetry is exhibited in nature such as in beehives, tree leaves, flowers, etc. Symmetrical designs are used by artists, professionals, designers of jewellery or clothing, car manufacturers and building architects, etc.

→ A symmetrical figure may have one or more than one line of symmetry. Also, a figure or an object that has line (s) of symmetry is said to have reflection symmetry.

Note:

1. Symmetry means the exact match in size and shape between two-halves, parts or sides of a figure or an object.

2. The line of symmetry can be real or imaginary.

3. Symmetrical figures having more than two lines of symmetry are said to be having multiple lines of symmetry. Sometimes a figure looks exactly the same when it is rotated by an angle about a fixed point. Such figures or objects are said to have rotational symmetry.

Such angle is called the angle of rotational symmetry of the figure. The fixed point of the figure about which the rotation occurs is called the centre of rotation.

Note: If a figure comes back to its original shape after one complete rotation through 360°, then the figure does not have rotational symmetry.

→ Both halves of a symmetrical shape match exactly when folded on the line of symmetry or axis of symmetry.

→ The line of symmetry acts as the mirror.

→ The mirror reflection and the line of symmetry are related to each other.

→ An isosceles triangle has only one line of symmetry.

→ A scalene triangle has no line of symmetry.

→ Regular polygons have equal sides and equal angles. They have more than one (multiple) lines of symmetry.

→ An equilateral triangle has three lines of symmetry.

→ A square has four lines of symmetry.

→ A regular pentagon has five lines of symmetry.

→ A regular hexagon has six lines of symmetry.

→ A circle has countless lines of symmetry.

→ The object and its image are symmetrical with reference to the mirror-line.

→ In a kaleidoscope usually two mirrors forming a V-shape are used. The angle between the mirrors determines the number of lines of symmetry.

→ If, after a rotation, an object looks exactly the same, it is said to have a rotational symmetry.

→ Some figures may have both lines of symmetry as well as angles of symmetry.

→ A quarter turn means 90°. A half-turn means a rotation by 180°. Three-quarter turn means 270°, and full turn means 360°.

## CBSE Class 6 Maths Chapter 9 Notes Symmetry

1. The objects or shapes with evenly balanced proportions are called symmetrical objects or shapes.

2. When a figure can be folded into two halves and both the halves overlap each other, the figure is said to be symmetrical.

3. The line along which the figure is folded is called lines of symmetry.

4. Line of symmetry can be horizontal, vertical or slant.