Theory question 109
Constructions(a) Using a ruler and a pair of compasses only construct triangle ABC with |AB| = 7.5cm, |BC| = 8.1cm and ∠ABC = 105°.
(b) Locate a point D on BC such that |BD| : |DC| is 3:2
(c) Through D, construct a line l perpendicular to BC.
(d) If the line l meets AC at P, measure |BP|
Show the model answer
Model answer
(a) Draw BC = 8.1 cm; construct 105° at B (90° + 15°, i.e. bisect between 90° and 120°); mark A with BA = 7.5 cm; join AC.
(b) Divide BC in the ratio 3 : 2: draw a line from B, step off 5 equal units, join the 5th to C and draw a parallel through the 3rd mark; BD ≈ 4.86 cm.
(c) Construct the perpendicular to BC at D.
(d) |BP| ≈ 5.4 cm
Explanation
Show all construction arcs; dividing a line in a ratio uses equal steps and parallel lines.