1. Draw a rectangle of diagonal 9 cm and angle between the diagonal and one side is 30°. Mark a point on the diagonal at a distance 6 cm from one end of the diagonal. Draw lines perpendicular to the sides of the rectangle through this point.
Erase unwanted parts, we get the required pattern.
2. Construct an equilateral triangle with side 3 cm.
The other two sides of a triangle are made by equal diagonals of the rectangle. Then the diagonal of the rectangle is 6 cm. Draw a rectangle in a horizontal position with diagonals 6 cm and the angle between the diagonals 60°. Draw another rectangle of the same measure in the vertical position at the middle of the first rectangle. Draw the wanted part in bold lines. Erase unwanted part.
3. Draw a rectangle ACBD, which diagonal (AB) is 6 cm and AC making an angle 30° with AB. The arc with centre at B and BC as radius and the arc with centre at A and AC as radi us meet at E. Complete ∆ AEB. Draw an arc with centre A and EB as radi us. Also draw arc with B as centre and AE as radius meet at F. Complete the rectangle AEBF.