Question

Construct a parallelogram ABCD, when AB = 5 cm, AC = 8 cm and BD = 9 cm.

Answer 1

Given:

• AB = 5 cm
• AC = 8 cm (diagonal)
• BD = 9 cm (diagonal)

Recall: In a parallelogram, the diagonals bisect each other. Let O be the intersection point of the diagonals AC and BD.

Therefore:

AO = OC

= `"AC"/2`

= `8/2`

= 4 cm

BO = OD

= `"BD"/2`

= `9/2`

= 4.5 cm

Steps of construction:

1. Draw a line segment AC of length 8 cm.
2. Find the midpoint O of AC by constructing its perpendicular bisector (O divides AC into two equal parts of 4 cm each).
3. With O as center, draw an arc with radius BO = 4.5 cm. This arc locates points B and D such that OB = OD = 4.5 cm.
4. At O, construct two points B and D on opposite sides of AC on the arc of radius 4.5 cm.
5. Join AB, BC, CD and DA to form the parallelogram ABCD.

The parallelogram ABCD is constructed with AB = 5 cm, diagonals AC = 8 cm and BD = 9 cm, where the diagonals bisect each other at point O.