Question

Construct a parallelogram PQRS, PQ = 4 cm, PR = 6 cm and QS = 8 cm.

Answer 1

Given:

• Parallelogram PQRS
• Side PQ = 4 cm
• Diagonal PR = 6 cm
• Diagonal QS = 8 cm

Steps of construction:

1. Draw a line segment PQ = 4 cm.
2. Since PR and QS are diagonals of the parallelogram and they bisect each other, let O be the intersection point of the diagonals.
3. Since PR = 6 cm, PO = OR = 3 cm (half of PR).
4. Since QS = 8 cm, QO = OS = 4 cm (half of QS).
5. At point P, draw an arc of radius 3 cm (for PO).
6. At point Q, draw an arc of radius 4 cm (for QO).
7. Let these arcs intersect at point O, the midpoint of both diagonals.
8. Using the midpoint O, construct the parallelogram by drawing the remaining vertices R and S, ensuring the diagonals bisect each other.
9. Join points PR and QS to complete parallelogram PQRS.

By drawing side PQ as 4 cm and locating point O by bisecting the diagonals PR = 6 cm and QS = 8 cm at half lengths, the parallelogram PQRS can be accurately constructed with its diagonals intersecting at O, maintaining the properties of a parallelogram.