Question

In the given figure AB = AC . if BE CF are the bisectors of Angle B and angle C respectively then prove that triangle EBC is congruent to triangle FCB

Answer 1

Answer:your answer is here

Answer 2

Answer:

AB = AC( Given )

Since  opposite angles of equal sides are equal

So, $\angle ACB = \angle ABC$   --A

Now we are given that BE and  CF are the bisectors of Angle B and angle C

So, $\angle ABE = \angle EBC = 2\angle ABC$  and   $\angle ACF = \angle FCB= 2\angle ACB$

Since $\angle ACB = \angle ABC$

So, $\frac{1}{2}\angle ACB = \frac{1}{2}\angle ABC$

$\angleFCB = \angle EBC$ ---B

In ΔEBC and ΔFCB

$\angle ECB = \angle FBC$ From A

BC = BC (common)

$\angleFCB = \angle EBC$ From B

So, ΔEBC ≅ ΔFCB by ASA property .