Mathematics
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 = 3.6 cm and angle B is obtuse.
Answer
Steps of construction :
Draw a line segment AB = 4.5 cm.
Draw ∠BAS = 120° and AE ⊥ AB.
From AE, cut AX = 3.3 cm.
Through X, draw a line PQ parallel to AB and cutting AS at D.
With B as center and radius equal to 3.6 cm draw an arc cutting PQ on C.
Join BC and CD.
Hence, ABCD is the required trapezium.
Related Questions
Using ruler and compasses, construct a rectangle ABCD, with AB = 5 cm and AD = 3.6 cm.
Using ruler and compasses only, construct the quadrilateral ABCD, having given AB = 5 cm, BC = 2.5 cm, CD = 6 cm, angle BAD = 90° and the diagonal AC = 5.5 cm.
Using ruler and compasses only, construct the quadrilateral ABCD, having given AB = 5 cm, BC = 2.5 cm, CD = 6 cm, ∠BAD = 90° and diagonal BD = 5.5 cm.
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AB = 6 cm, AD = 3 cm and ∠DAB = 45°. If the bisector of ∠DAB meets DC at P, prove that ∠APB is a right angle.