Question

In ΔABC, ray BD bisects ∠ABC and ray CE bisects ∠ACB.If seg AB≅seg AC then prove that ED||BC.

Answer 1

Steps:
1) Since, Ray BD bisects ∠ ABC  :
By Angle Bisector Theorem , 
  $\frac{AB}{AD} = \frac{BC}{CD} --(1)$ 

 Similarly,
 $\frac{AC}{AE} = \frac{BC}{BE} --(2 )$

2) It is given that , AB =AC and using above two equations ,we get :
 
$\frac{AE}{BE} = \frac{AD}{CD}$ 

=> Ratio of segments on both sides are proportional .
=> By Converse of Thales Theorem , 
   ED || BC  

Hence Proved :