Question

In right triangle ABC AB=BC .If bisector of angle A meets BC at D. Prove that BC=2AD

Answer 1

ln Δ , ABC right angled at A and AB = AC

Hence ∠ A = ∠ B

We know that Sum of angles of a triangle = 180º

∠A+ ∠B+ ∠C=180º

90º+∠B+∠B=180º

2∠B=180º -90º

2∠B=90º

∠B=45º………………………………………..(i)

ALSO , AD is the bisector of BAC

So , ∠BAD = ∠CAD = 90º/2 = 45º …………………………….(ii)

∠BAD = ∠ABC

SO, AD = BD ………………………………(iii) .

Similarly angle CAD = angle ACD

So, AD = DC ………………………………..(iv)

adding equation (iii) and (iv)

We will get, AD + AD = BD+DC

2AD = BC