 # Symmetry and Reflection

## The linear symmetry is a symmetry in which a line divides a given figure into two identical halves. The line is called the axis of symmetry or line of symmetry. A figure is said to have point symmetry about a point called the centre of the figure, if for every point on the figure, there is another point directly opposite to it on the other side of centre. The concept of line symmetry is closely related to mirror reflection. When a point is being reflected on a line then, the line acts as a mirror and the image of the point is obtained at the same distance on the opposite side of the line. This line is then called the axis of symmetry or line of reflection. When a point is reflected in x-axis, then its x-coordinate remain same and sign of y-coordinate changes. When a point is reflected in y-axis, then its y-coordinate remain same and sign of x-coordinate changes. A point which remains unaltered under a transformation is called an invariant point. Reflection is a transformation in which the figure is the mirror image of the other.

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• Q1

A line segment is symmetrical about its

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perpendicular bisector.

##### Explanation: In the above figure a line segment AB is symmetrical about its perpendicular bisector.

• Q2

In PQR if, PQ = QR = PR = 4.4 cm and PQR=60°. The triangle has/have

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three lines of symmetry.

##### Explanation: Since the triangle PQR is an equilateral triangle. Hence, there will be three lines of symmetry.

• Q3

An isosceles triangle has/have

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one line of symmetry.

##### Explanation: • Q4

An equilateral triangle has

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three lines of symmetry.

##### Explanation: • Q5

A scalene triangle has

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no lines of symmetry.

##### Explanation:

We cannot have a line in a scalene triangle about which if the triangle is folded such that the two parts of the figure will coincide. Scalene triangle