## NCERT 6TH CLASS MATHEMATICS CHAPTER SYMMETRY

**INTRODUCTION**

**INTRODUCTION**

The world is full of beautiful things. Some of them are natural, whereas some of them are man made. Many of these things are beautiful because they possess symmetry. Symmetry refers to the exact match in shape and size between two halves of an object. That is if we fold a picture in half and both the halves – left half and right half – match exactly then we can say that the picture is symmetrical.

**Reflection Symmetry :**

If we draw a vertical line at the middle, the portions on either side of the line are identical. Similarly, in nature we find many flowers, leaves, etc., that have two identical sides if we draw a line through the middle of them.

**Mirror Symmetry :**

Reflection symmetry is the symmetry with respect to reflection. If a mirror is placed along the line at the middle, the half part of the figure reflects through the mirror creating the remaining identical half. In other words, the line where the mirror is placed divides the figure into two identical parts they are of the same size and also every specific part on one side of the line will have its reflection exactly at the same distance on the other sides. Thus, it is also known as mirror symmetry or mirror image symmetry.

**Line of Symmetry or Axis of Symmetry**

The line AB divides the given figures into two identical parts. If a figure is folded along the line AB, one half of the figure will coincide exactly with the other half. In other words, one half is the mirror image of the other half. In such cases we say that the figure is symmetrical and the line which divides the figure into two identical parts is called the line of symmetry or the axis of symmetry.

**Two or more lines of symmetry**

Some objects and figures have no line of symmetry, a scalene triangle is not symmetrical. We can say that a scalene triangle is asymmetrical.

**(a) Scalene triangle (b) Irregular shape**

Some objects and figures have more than one line of symmetry.

Through this isosceles triangle you can draw one line of symmetry.

**A rectangle has two lines of symmetry.**

If we take an equilateral triangle, we can find that three lines of symmetry can be drawn through the triangle

A square would have four lines of symmetry,

A circle has infinite lines of symmetry

**OBJECTIVE TYPE**

Q.1 Which of the following letters does not have any line symmetry?

(A) H (B) V (C) Z (D) l

Q.2 A rhombus is symmetrical about :

(A) each of its diagonals

(B) the line joining the midpoints of opposite sides

(C) perpendicular bisector of each of the sides

(D) None of these