# Symmetry

**Exercise 1**

**1. **Copy the figures with punched holes and find the axes of symmetry for the following:

**2. ** Given the line(s) of symmetry, find the other hole(s):

**3.** In the following figures, the mirror line (i.e. the line symmetry) is given as a dotted line. Complete each figure performing reflection in the dotted (mirror) line. (You might perhaps place a mirror along the dotted line and look into the mirror for the image). Are you able to recall the name of the figure you complete?

**4.**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:

**5. ** 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 diagonal?

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

**7.**State the number of lines of symmetry for the following figures:

(a) An equilateral triangle (b) An isosceles triangle (c) A scalene traingle

(d) A square (e) A rectangle (f) A rhombus

(g) A parallelogram (h) A quadrilateral (j) A regular hexagon

(j) A circle

**8. ** What letters of the English alphabet have reflectional symmetry (i.e., symmetry related to mirror reflection) about:

(a) a vertical mirror

(b) a horizontal mirror

(c) both horizontal and vertical mirrors

**9.** Give three examples of shapes with no line of symmetry. **10. ** What other name can you give to the line of symmetry of:

(a) an isosceles triangle?

(b) a crcrle?

**Exercise 2**

**11.** Which of the following figures have rotational symmetry of order more than 1:

**12. ** Give the order the rotational symmetry for each figure:

**Exercise 3**

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

**14. ** 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

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

**15. ** In a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?

**16. ** Fill in the blanks:

**17. **Name the quadrilateral which has both line and rotational symmetry of order more than 1.

**18. ** 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?

**19. ** Can we have a rotational symmetry of order more than 1 whose angle of rotation is:

(i) 45° (ii) 17° ?