If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?

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Solution

In case of rectangle, we have
Number of line of symmetry = 2
Order of rational symmetry = 2
In case of equilateral triangle, we have

Number of line of symmetry = 3
Order of rational symmetry = 3
In case of circle, we have
Number of line of symmetry = infinite
Order of rational symmetry = infinite
Yes. If a figure has two or more lines of symmetry, then it will definitely have its rotational symmetry of order more than 1.

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Identify a quadrilateral with a rotational symmetry of order more than 1 but does not have a line symmetry.

Draw, wherever possible, a rough sketch of

(i) a triangle with both line and rotational symmetries of order more than 1.

(ii) a triangle with only line symmetry and no rotational symmetry of order more than 1.

(iii) a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.

(iv) a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

A figure with angle of rotation as $17^{\circ}$ has rotational symmetry of order more than 1. Say true or false.

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