Question

Construct a parallelogram ABCD, when AC = 9 cm, BD = 8 cm and ∠BOC = 45°.

Answer 1

Given:

• Diagonal AC = 9 cm
• Diagonal BD = 8 cm
• ∠BOC = 45° where O is the intersection point of diagonals AC and BD in parallelogram ABCD

Steps of construction:

1. Draw the diagonal AC = 9 cm.
2. Draw the perpendicular bisector of AC and mark the midpoint as O (since diagonals bisect each other, O is midpoint of AC).
3. At point O, construct the angle ∠BOC = 45°.
4. On one ray of this angle, cut off OB = OD = `(BD)/2 = 8/2` = 4 cm from O.
5. Extend BO to D such that OD = 4 cm.
6. Join points A and B, B and C, C and D and A and D to form parallelogram ABCD.

The required parallelogram ABCD is constructed with given diagonals and ∠BOC = 45°, ensuring diagonals bisect each other at O and the angle between them is as given.