Question

Abc is a right triangle with ab = ac. Bisector of angle a meets bc at d prove that bc = 2 ad.

Answer 1

Answer:

Step-by-step explanation:

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

=> ∠ A = ∠ B 

∠A+ ∠B+ ∠C=180º   (∵Sum of angles of a triangle = 180º) 

90º+∠B+∠B=180º 

2∠B=180º -90º 

2∠B=90º 

∠B=45º………………………………………..(i) 

Given , AD is the bisector of ∠BAC 

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

∠BAD = ∠ABC 

=> AD = BD ………………………………(iii) . 

Similarly ∠CAD = ∠ACD 

=>, AD = DC ………………………………..(iv) 

adding equation (iii) and (iv) 

We will get, AD + AD = BD+DC 

=> 2AD = BC