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Symmetry

Question

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

Solution

Yes. If a figure has two or more lines of symmetry, then it will definitely have its rotational symmetry of order more than 1.

Some More Questions From Symmetry Chapter

Copy the figure given here.
Take any one diagonal as a line of symmetry and shade a few more squares to make the figure symmetric about a diagonal. Is there more than one way to do that? Will the figure be symmetric about both the diagonals?

Copy the diagram and complete each shape to be symmetric about the mirror line (s):

State the number of lines of symmetry for the following figures:
(a) An equilateral triangle
(b) An isosceles triangle
(c) A scalene triangle
(d) A square
(e) A rectangle
(f) A rhombus
(g) A parallelogram
(h) A quadrilateral
(i) A regular hexagon
(j) A circle

Give three examples of shapes with no line of symmetry.

What other name can you give to the line of symmetry of
(a) an isosceles triangle?
(b)a circle?

Give the order of rotational symmetry for each figure:

Name any two figures that have both line symmetry and rotational 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.

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

Fill in the blanks:

Shape Centre of Rotation Order of Rotation Angle of Rotation

Square
–

–

–

Rectangle
–

–

–

Rhombus
–

–

–

Equilateral Triangle
–

–

–

Regular Hexagon
–

–

–

Circle
–

–

–

Semi-circle
–

–

–

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