Question

Angle B is equals to angle C and ab is equals to AC prove that triangle ABC is congruent to triangle ACE​

Answer 1

Answer:

ANSWER

Since the angles opposite to equal sides are equal,

∴AB=AC

⇒∠C=∠B

⇒2∠B=2∠C.

Since BO and CO are bisectors of ∠B and ∠C, we also have 

∠ABO=2∠B and ∠ACO=2∠C.

∠ABO=2∠B=2∠C=∠ACO.

Consider △BCO:

∠OBC=∠OCB    

⇒BO=CO ....... [Sides opposite to equal angles are equal]

Finally, consider triangles ABO and ACO.

BA=CA ...... (given);

BO=CO ...... (proved);

∠ABO=∠ACO    (proved).

Hence, by S.A.S postulate

△ABO≅△ACO

⇒∠BAO=∠CAO⇒AO bisects ∠A.