Question

Construct a △ ABC in which base AB = 5cm, ∠A = 30° and AC – BC = 2.5cm. Justify your construction.

Answer 1

Steps of Construction:

Construct AB = 5 cm

Construct ∠BAX = 30^o

From AX, cut the line segment AD which is equal to AC – BC = 2.5 cm

Join the points BD

Construct a perpendicular bisector of BD which meets AX at the point C

In order to obtain the required triangle ABC join BC

Justification:

We know that C lies on BD which is the perpendicular bisector

So we get

CD = BC

We know that AD = 2.5 cm

It can be written as

AC – CD = 2.5 cm

So we get

AC – BC = 2.5 cm

Therefore, △ ABC is the required triangle.