Theory question 110
Constructions(a) Using ruler and a pair of compasses only, construct: (i) quadrilateral PQRS such that |PQ| = 10 cm, |QR| = 8 cm, |PS| = 6 cm, ∠PQR = 60° and ∠QPS = 75°; (ii) the locus l1 of points equidistant from QR and RS; (iii) locus l2 of points equidistant from R and S.
(b) Measure |RS|.
Show the model answer
Model answer
(a)(i) Draw PQ = 10 cm. Construct 60° at Q and mark QR = 8 cm; construct 75° at P (60° + half of 30°) and mark PS = 6 cm. Join RS.
(ii) l1 is the bisector of ∠QRS.
(iii) l2 is the perpendicular bisector of RS.
(b) |RS| ≈ 4.6 cm.
Explanation
Points equidistant from two lines lie on the bisector of the angle between them.