Construction (II)

Reference: Study Notes (last section) Practice Questions on Geometrical Construction

Question 1
Draw ∆ ABC in which AB = 9.0 cm, AC = 6.5 cm and BC = 10.6 cm.
On your drawing, construct
(a) the perpendicular bisector of the side AB
(b) the angle bisector of angle BAC


View clip to see how to construct the diagram


Question 2
The following shows a regular polygon. 
Using ruler and compasses only, construct the 
(a) bisector of obtuse angle CDE and
(b) equilateral triangle CXD, with X below CD

Measure 
(a) length of AB
(b) obtuse angle ABC
(c) name the polygon


View clip to see how to construct the diagram




Question 3
The diagram shows a triangle PQR. On the diagram
(a) Construct the angle bisector of angle PRQ
(b) Construct the perpendicular bisector of PR
(c) Mark with a letter X the point where your answers in part (a) and (b) meet
(d) What can you say about angle XPQ and angle XQP?


View clip to see how to construct the diagram



Question 4
Draw and label the locus of points within the triangle which are
(a) 8 cam from A
(b) 2.5 cm from AB
(c) equidistant from A and B
(d) equidistant from AB and BC

A point Q is such that AQ < 8 cm, more than 2.5 cm from AB, is nearer to A than B and nearer to AB than BC. Shade the region in which Q must be.



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