Theory question 108
Constructions(a) Using ruler and a pair of compasses only, construct a: (i) trapezium WXYZ such that |WX| = 8 cm, |XY| = 5.5 cm, |XZ| = 8.3 cm, ∠WXY = 60° and WX//ZY; (ii) rectangle PQYZ where P and Q are on WX.
(b) Measure: (i) |QX| (ii) ∠XWZ.
Show the model answer
Model answer
(a)(i) Draw WX = 8 cm; construct 60° at X and mark Y with XY = 5.5 cm; through Y construct a line parallel to WX; with centre X and radius 8.3 cm cut this line at Z; join WZ.
(ii) Drop perpendiculars from Z and Y to WX, meeting it at P and Q; PQYZ is the rectangle.
(b)(i) |QX| ≈ 2.8 cm (± 0.1) (ii) ∠XWZ ≈ 76° (± 1°)
Explanation
Keep construction arcs visible; measured answers within ± 0.1 cm and ± 1° are accepted.