Page 5 - ln1

Solution: It is given that AB = AC and the bisectors ∠ B and ∠ C meet at a point O
Consider △ BOC
So we get
∠ BOC = ½ ∠ B and ∠ OCB = ½ ∠ C
It is given that AB = AC so we get ∠ B = ∠ C
So we get∠ OBC = ∠ OCB
We know that if the base angles are equal even the sides are equal
So we get OB = OC ……. (1)
∠ B and ∠ C has the bisectors OB and OC so we get
∠ ABO = ½ ∠ B and ∠ ACO = ½ ∠ C
So we get∠ ABO = ∠ ACO …….. (2)
Considering △ ABO and △ ACO and equation (1) and (2)
It is given that AB = AC
By SAS congruence criterion
△ ABO ≅△ ACO
∠ BAO = ∠ CAO (c. p. c. t)
Therefore, it is proved that BO = CO and the ray AO is the bisector of ∠ A.