Question

Construct a parallelogram ABCD, when BC = 5 cm, BD = 4 cm and altitude on BC = 2 cm.

Answer 1

Given:

• BC = 5 cm
• BD = 4 cm
• Altitude on BC = 2 cm

Steps of construction:

1. Draw the base BC = 5 cm.
2. At point B, draw a perpendicular line to BC because the altitude is perpendicular to BC.
3. On this perpendicular line at B, mark point E such that BE = 2 cm altitude.
4. Draw a line parallel to BC through point E.
5. With B as the center and radius BD = 4 cm, draw an arc cutting the parallel line at point D.
6. Join points C and D.
7. With D as center and radius equal to BC = 5 cm, draw an arc cutting the extension of line AB at point A.
8. Join A to B and A to D.

The quadrilateral ABCD constructed with these steps is the required parallelogram having BC = 5 cm, diagonal BD = 4 cm and the altitude on BC = 2 cm.