Question

In a triangle ABC, D is the midpoint of side AC such that BD =1/2 AC. Show that angle ABC is a right angle.

Answer 1

AD+DC =AC, so that BD = 1/2 Ac

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.