Theory question 108
ConstructionsABCD is a trapezium in which AB||DC, |AB| = 8cm, ∠ABC = 60°, |BC| = 5.5cm and |BD| = 8.3cm.
(a) Using a ruler and a pair of compasses only, construct (i) the trapezium ABCD; (ii) a rectangle PQCD, where P, Q are two points on AB.
(b) Measure |AC| and |QB|
Show the model answer
Model answer
(a)(i) Draw AB = 8cm; construct 60° at B and mark C with BC = 5.5cm; construct a line through C parallel to AB; with centre B and radius 8.3cm cut this line at D; join AD. Construction arcs must be shown.
(ii) Drop perpendiculars from D and C to AB, meeting AB at P and Q; PQCD is the rectangle.
(b) |AC| ≈ 7.1cm; |QB| ≈ 2.75cm (accept 2.7−2.8cm)
Explanation
To draw the parallel through C, copy the angle at B or construct two perpendiculars.