Construct a quadrilateral ABCD in which AB = 6.5 cm.BC = 5.4 cm, CD = 5.8 cm, DA = 7.3 cm and ∠B = 60. Construct a quadr

Solution

Given: Sides of a quadrilateral ABCD as  AB = 6.5 cm. BC = 5.4 cm, CD = 5.8 cm, DA = 7.3 cm and ∠B = 60o.

Required: To construct quadrilateral similar to quadrilateral ABCD, whose sides are th of the corresponding sides of ABCD, i.e. quadrilateral A′BC′D′ in which and .

Steps of Construction:

1. Draw the line segment BC = 5.4 cm.

2. At B, construct angle YBC = 60o.

3. With centre B and radius equal to 6.5 cm, draw an arc cutting YB at A.

4. With centre A and radius equal to 7.3 cm, draw an arc.

5. With centre C and radius equal to 5.8 cm, draw another arc cutting the previous arc at D

6. Join AD and CD.

Then ABCD is the required quadrilateral.

7. Join BD.

8. Draw any ray BX inclined at certain acute angle with BD on the opposite sides of A.

9. Starting from B, cut off five equal line segments and on BX.

10. Join and draw a line segment parallel to to intersect at D′.

11. Draw a line D′A′ parallel to DA which intersects AB at A′.

12. Draw a line D′C′ parallel to DC which intersects BC at C′.

Then A′BC′D′ is the required quadrilateral similar to quadrilateral ABCD.