Question

The perpendicular distance between the pair of opposite sides of a parallelogram are 3 cm and 4 cm, and one of its angles measures 60^o. Using a ruler and compasses only,
construct the parallelogram.

Answer 1

Steps:
1. Draw a baseline AQ.

2. A take some random distance in compass and draw one are below and above the line. Now without changing the distance in compass draw one are below and above the line. These arcs intersect each other above and below the line. Draw the line passing through these intersecting points, you will get perpendicular to the line AQ.

3. Take distance of 4 cm in compass and mark an arc on the perpendicular above the line. Draw a line parallel to line AQ passing through this arc.

4. From point A measure an angle of 60 degrees and draw the line which intersects the above-drawn line at some point label it as D.

5. Using the procedure given in step 2 again draw a perpendicular to line AD.

6. Take distance of 3 cm in compass and mark an arc on the perpendicular above the line. Draw a line parallel to line AD passing through this arc which intersects the line AQ at some point label it as B and to other lines at point C.

ABCD is the required parallelogram.