Theory question 110
ConstructionsUsing ruler and a pair of compasses only. (a) construct: (i) ΔXYZ such that |XY| = 10 cm, ∠XYZ = 30° and ∠YXZ = 45°; (ii) locus, l1, of points equidistant from Y and Z; (iii) locus, l2, of points parallel to XY through Z. (b) Locate point M, the point of intersection of l1 and l2. (c) Measure ∠ZMY.
Show the model answer
Model answer
(a)(i) Draw XY = 10 cm; construct 30° at Y and 45° at X; the arms meet at Z.
(ii) l₁ is the perpendicular bisector of YZ.
(iii) l₂ is the line through Z parallel to XY (e.g. copy the angle at Y onto Z).
(b) M is where l₁ meets l₂.
(c) ∠ZMY ≈ 120° (MZ = MY and ∠MZY = 30°, so ∠ZMY = 180° − 60°); accept 120° ± 1°.
Explanation
Leave all construction arcs showing.