Question

Construct a △ ABC in which BC = 4.5cm, ∠B = 45° and AB + AC = 8cm. Justify your construction.

Answer 1

Steps of Construction:

Construct a line BC = 4.5 cm

Construct ∠CBX = 45^o

From BX, cut the line segment BD which is equal to AB + AC = 8 cm

Join the points CD

Construct a perpendicular bisector of CD which meets BD at the point A

In order to obtain the required triangle ABC join CA

Justification:

We know that A lies on CD which is the perpendicular bisector

So we get

AC = AD

We know that BD = 8cm

It can be written as

BA + AD = 8cm

So we get

AB + AC = 8cm

Therefore, △ ABC is the required triangle.