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Step-by-step explanation:
ab=ac (the triangle is isoceles)
therefore b =c
obc = ocb ( ob and oc bisect angle b and c respectivly)
ob=oc ( sides opposite to equal angles are equal)
ii) in triangle aob and OC
ob=oc
ab=ac
abo=aco
by SAS congruency,these triangles are congruent
bao=Cao
therefore ao bisect angle a
Answer:
given :- AB = AC, also < B = < C ( angles opposite to equal sides are equal )
to prove :- 01 - OB = OC, 02 -AO bisects < A
proof :- in triangle ABO and triangle ACO
1 . AB =AC (given)
2 . < B = < C (given)
then, 1/2 < B = 1/2 < C
<ABO=<ACO
3 . AO = AO (common)
hence , triangle ABO congruent to triangle ACO
now , OB = OC ( by CPCT )
also, we can prove <BAO = <CAO ( BY CPCT ) - 1
therefore, from 1 we get that AO bisects <A.
hence proved.