Chapter 12, Problem 16CT

To determine

To identify : If the given figure has any rotational symmetry. To draw lines of symmetry and if the figure has rotational symmetry, give each angle and direction of rotation.

Answer to Problem 16CT

The given figure has $3$ lines of symmetry that are shown in dotted line.

The given figure has $3$ rotational symmetry.

$1$ st rotational symmetry: rotation of ${120}^{\circ }$ counter clockwise (or clockwise)

$2$ nd rotational symmetry: rotation of ${240}^{\circ }$ counter clockwise (or clockwise)

$3$ rd rotational symmetry: rotation of ${360}^{\circ }$ counter clockwise (or clockwise)

Explanation of Solution

Given information : Lines of symmetry and rotational symmetry are to be found in the given figure.

Formula used :

A figure has line symmetry if a line called the line of symmetry, divides the figure into two part that are reflection of each other in the line.

A figure has rotational symmetry if a rotation of ${180}^{\circ }$ or less clockwise (or counter clockwise) about its center produces an image that fits exactly on the original figure.

The given figure has $3$ lines of symmetry that are shown in dotted line.

The given figure has $3$ rotational symmetry.

$1$ st rotational symmetry: rotation of ${120}^{\circ }$ counter clockwise (or clockwise)

$2$ nd rotational symmetry: rotation of ${240}^{\circ }$ counter clockwise (or clockwise)

$3$ rd rotational symmetry: rotation of ${360}^{\circ }$ counter clockwise (or clockwise)