Question

Construct a parallelogram ABCD, when AC = 10 cm, BD = 8.6 cm and ∠BOC = 30°.

Answer 1

Given:

• Diagonal AC = 10 cm
• Diagonal BD = 8.6 cm
• Angle between diagonals ∠BOC = 30°, where O is the intersection point of diagonals AC and BD

Steps of construction:

1. Since diagonals of a parallelogram bisect each other, find the half-lengths of diagonals:

`AO = OC = (AC)/2 = 10/2 = 5` cm

`BO = OD = (BD)/2 = 8.6/2 = 4.3` cm

2. Draw diagonal AC = 10 cm and mark its midpoint O.

3. At point O, construct ∠BOC = 30°.

4. From point O on the constructed angle, measure BO = 4.3 cm along one arm of the angle.

5. Mark this point as B. Extend BO to D such that OD = 4.3 cm on the opposite side of O along the same line.

6. Join points A to B, B to C, C to D and D to A.

ABCD is the required parallelogram with diagonals AC = 10 cm and BD = 8.6 cm and the angle between diagonals ∠BOC = 30°.