Question

ABC is a right angle triangle in which AB = AC. The bisector of angle A meets BC at D.Prove that BC = 2AD

Answer 1

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

Giben ∠ A = ∠ B

∠A+ ∠B+ ∠C=180º [We know that Sum of angles of a triangle = 180º]

90º+∠B+∠B=180º  [∠ A = ∠ B ]

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  Prooved