Question

AB and AC are equal sides of an isosceles triangleABC.if the bisectors of angleABC and angleACB intersect each at O, triangleAOB is congruent to triangle AOC.​

Answer 1

Answer:

Step-by-step explanation:

In △ABC, we have  

AB=AC

⇒∠C=∠B ∣ Since angles opposite to equal sides are equal

⇒  

2

1

​

∠B=  

2

1

​

∠C

⇒∠OBC=∠OCB

⇒∠ABO=∠ACO    …(1)

⇒OB=OC ∣ Since sides opp. to equal ∠s are equal     …(2)

(ii) Now, in △ABO and △ACO, we have  

AB=AC ∣ Given

∠ABO=∠ACO ∣ From (1)

OB=OC ∣ From (2)

∴ By SAS criterion of congruence, we have  

△ABO≅△ACO

⇒∠BAO=∠CAO ∣ Since corresponding parts of congruent triangles are equal

⇒ AO bisects ∠A