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Symmetry

Question

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Give three examples of shapes with no line of symmetry.

Solution

A scalene triangle, a parallelogram, and a trapezium do not have any line of symmetry.

Some More Questions From Symmetry Chapter

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
–

–

–

Name the quadrilaterals which have both line and rotational symmetry of order more than 1.

After rotating by 60° about a centre, a figure looks exactly the same as its original position. At what other angles will this happen for the figure?

Can we have a rotational symmetry of order more than 1 whose angle of rotation is
(i) 45°?
(ii) 17°?

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