Question

Using ruler and compasses only, construct a trapezium ABCD, in which the parallel sides AB and DC are 3.3 cm apart; AB = 4.5 cm, angle A = 120° BC = 4.2 cm and angle B is obtuse.

Answer 1

Steps:

1. Draw line segment AB = 4.5 cm.
2. Construct ∠XAB = 90° at point A, mark point X such that AX = 3.3 cm on the perpendicular ray.
3. Through X, draw a line PQ parallel to AB.
4. Construct ∠BAS = 120° at point A, with the ray AS intersecting line PQ at point D. (Join AD).
5. With center B and radius 4.2 cm, draw a dashed arc (compass work) to intersect line PQ at point C. Choose the point C that makes angle B obtuse.
6. Join BC.
7. ABCD is the required trapezium with all specified parameters and angle B being obtuse.