Question

19. In a triangle ABC, the bisectors of angle ABC and angle ACB meet at O.IF OB = OC, prove that triangle ABC is an isosceles
triangle.​

Answer 1

Answer:

we can say that angle obc =angle ocb.(as the base angles of an isosceles triangles are equal.)

let both angle obc and angle ocb be x,then angle abc=angle Acb=2x

we know that the base angles of an isosceles triangle are equal,and the base. angles of triangle abc are equal.

hence proved

Answer 2

Answer:

given OB=OC

  i.e, ΔOBC is isosceles

to prove ABC is isosceles

in  ΔOBC  OB =OC

        ∠OBC=∠OCB

       ∠OAB = ∠OBC

∠ AOB =∠ OBC .....(i)

and  ∠ ACO = ∠ OCB ....(ii)

Adding (i) and (ii) we get

∠ AOB + ∠ ACO =  ∠ OBC +  ∠ OCB

∠ ABC = ∠ ACB

AB = AC                                     opposite sides of an equal angles

Hence, triangle ABC is an isosceles triangle.