Question

in a triangle ABC D is the midpoint of side AC such that BD equal to 1 by 2 AC so that angle abc is a right angle triangle

Answer 1

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Here is your answer.

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.