Question

Construct a triangle BCP given BC= 5 cm, BP= 4 cm and $\angle PBC={45}^o$.

(i) Complete the rectangle ABCD such that:

(a) P is equidistant from AB and BC.

(b) P is equidistant from C and D.

(ii) Measure and record the length of AB.

Answer 1

i) Steps of Construction:

1) Draw a line segment BC = 5 cm

2) B as centre and radius 4 cm draw an arc at an angle of 45 degrees from BC.

3) Join PC.

4) B and C as centers, draw two perpendiculars to BC.

5) P as centre and radius PC, cut an arc on the perpendicular on C at D.

6) D as centre, draw a line parallel to BC which intersects the perpendicular on B at A.

ABCD is the required rectangle such that P is equidistant from AB and BC (since BD is angle bisector of angle B) as well as C and D.

ii) On measuring AB = 5.7 cm