Theory question 109
Constructions(a) Using ruler and a pair of compasses only, construct: (i) a trapezium WXYZ such that |WX| = 10.2 cm, |XY| = 5.6 cm, |YZ| = 5.8 cm, ∠WXY = 60° and WX is parallel to YZ; (ii) a perpendicular from Z to meet WX at N.
(b) Measure: (i) |WZ|; (ii) |ZN|.
Show the model answer
Model answer
(a)(i) Draw WX = 10.2 cm; construct 60° at X and mark XY = 5.6 cm. Through Y draw a line parallel to WX (e.g. construct 120° at Y) and mark YZ = 5.8 cm towards W. Join WZ.
(ii) From Z construct the perpendicular to WX, meeting it at N.
(b)(i) |WZ| ≈ 5.1 cm. (ii) |ZN| ≈ 4.8 cm (= 5.6 sin 60° ≈ 4.85 cm).
Explanation
Co-interior angles: if ∠X = 60°, the angle at Y between YX and YZ is 120°.