Question

Construct a parallelogram ABCD, when AB = 6 cm, AC = 7 cm and BD = 9.4 cm.

Answer 1

Given:

• Side AB = 6 cm
• Diagonal AC = 7 cm
• Diagonal BD = 9.4 cm

Steps of construction:

1. Let O be the point of intersection of the diagonals AC and BD.

2. Since diagonals of a parallelogram bisect each other

`AO = OC = (AC)/2 = 7/2 = 3.5` cm

`BO = OD = (BD)/2 = 9.4/2 = 4.7` cm

3. Draw segment AB = 6 cm.

4. At B, draw arcs with radius BO = 4.7 cm.

5. At A, draw arcs with radius AO = 3.5 cm.

6. The intersection of the two arcs will give the point C.

7. Join AC and BC.

8. Similarly, with center A, radius equal to `(BD)/2` = 4.7 cm and with center B, draw arcs to locate point D such that BD = 9.4 cm.

9. Join AD and DC.

10. This completes the parallelogram ABCD.