Symmetry

• Line Symmetry
  If a figure is divided into two coincident parts by a line, then the figure is called symmetrical about that line, and the line is its line (or axis) of symmetry.
• Point Symmetry
  A figure is said to have a point symmetry if every line segment joining two points of the figure and passing through the point is bisected at that point, and the point is called center of symmetry of the figure.

Exercise

1. Construct an equilateral triangle with side 5 cm and draw all its lines of symmetry.
2. Construct an isosceles triangle with base 4·4 cm and base angle = 75°. Draw its line of symmetry.
3. Construct an angle of 135° and draw its axis of symmetry.
4. Construct a regular hexagon with side 2·8 cm and draw all its lines of symmetry. Indicate the point of symmetry with letter O.
5. Construct a rhombus ABCD of side 4·6 cm and BCD = 135° by using ruler and compasses only. Indicate its point of symmetry with the letter O.
6. Using ruler and compasses only, construct a rectangle ABCD with AB = 6 cm and AD = 4 cm. Also construct its lines of symmetry.
7. Construct a rectangle ABCD with AB = 4 cm and AC = 5 cm (steps of construction need not be written but the lines of construction must be shown clearly). Also draw all lines of symmetry of the rectangle ABCD, and indicate the point of symmetry with the letter O.
8. Construct ABC in which AB = AC = 3·5 cm and BC = 4·5 cm. Draw the reflection D of A in the line BC.Draw the lines of symmetry of the quadrilateral ABDC. Assign the special name to quadrilateral ABDC.
9. Draw neat diagrams showing the line (or lines) of symmetry; if any, and give the specific name of the quadrilateral.
   (i) Quadrilateral having no line of symmetry but having the point of symmetry.
   (ii) Quadrilateral having only one line of symmetry. How many such quadrilaterals are there?
   (iii) Quadrilateral having its diagonals as the only lines of symmetry.
   (iv) Quadrilateral with equal diagonals and having only two lines of symmetry.
   (v) Quadrilateral having more than two lines of symmetry.

Answers