Question

in triangle ABC ray BD bisects angle ABC and ray CE bisects ANGLEACB. If segment AB congruent seg AC then prove that ED IS parallel to BC

Answer 1

i hope it will helpful to you.

Answer 2

Answer:

Step-by-step explanation:

It is given that in ΔABC ray BD bisects  ∠ABC and ray CE bisects ∠ACB and AB=CD.

From ΔABC, BD is the bisector of ∠ABC, then by using angle bisector theorem, we have

$\frac{AD}{DC}=\frac{AB}{BC}$               (1)

Also, CE is the angle bisector of ∠ACB, thus

$\frac{AE}{EB}=\frac{AD}{BC}$                (2)

Also, we are given that AB=CD, then from (1),(2)and (3)

$\frac{AE}{EB}=\frac{AD}{DC}$

which implies that segment ED is parallel to segment BC by the converse of basic proportionality theorem.

Hence proved.