Question

In a triangle abc, d is the mid-point of side ac such that bd = 1 2 ac. show that ∠abc is a right angle.

Answer 1

I hope this will help you

Answer 2

In ΔADB, AD = BD

∠DAB = ∠DBA = ∠x ( these are the angles which have opposite sides)

In ΔDCB, BD = CD

∠DBC = ∠DCB = ∠y

In ΔABC we will use the angle sum property

∠ABC + ∠BCA + ∠CAB = 180°

2(∠x + ∠y) = 180°

∠x + ∠y = 90°

∠ABC = 90°

This means that ABC is the right angled triangle.