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Symmetry
The following figures have more than one line of symmetry. Such figures are said to have multiple lines of symmetry.
Identify multiple lines of symmetry, if any, in each of the following figures:
(a) The given figure has 3 lines of symmetry. Hence, it has multiple lines
of symmetry.
(b) The given figure has 2 lines of symmetry. Hence, it has multiple lines
of symmetry.
(c) The given figure has 3 lines of symmetry. Hence, it has multiple lines
of symmetry.
(d)The given figure has 2 lines of symmetry. Hence, it has multiple lines
of symmetry.
(e) The given figure has 4 lines of symmetry. Hence, it has multiple lines
of symmetry.
(f) The given figure has only 1 line of symmetry.
(g) The given figure has 4 lines of symmetry. Hence, it has multiple lines
of symmetry.
(h) The given figure has 6 lines of symmetry. Hence, it has multiple lines
of symmetry.
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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 |
– |
– |
– |
Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
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