Theory question 113
Constructions(a) Using a ruler and a pair of compasses only, construct ΔMNR in which |MN| = 8.7 cm, |MR| = 10.5 cm and ∠MNR = 75°.
(b) Locate by construction, a point S such that RS is parallel to MN and S is equidistant from points M and R.
(c) Measure: (i) |NR|; (ii) ∠NRS
(d) What shape is SMNR?
Show the model answer
Model answer
(a) Draw MN = 8.7 cm; at N construct 75° (60° + half of 30°); with centre M and radius 10.5 cm cut the arm at R; join MR
(b) Construct the line through R parallel to MN and the perpendicular bisector of MR; S is where they meet
(c)(i) |NR| ≈ 8.5 cm (ii) ∠NRS ≈ 105° (allow ±1)
(d) SMNR is a trapezium (RS ∥ MN)
Explanation
RS ∥ MN, so ∠NRS and ∠MNR are co-interior angles adding to 180°.