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Symmetry
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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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