in a triangle abc ,the bisector of angle abc and angle acb meet at o,if ob=oc,rove that triangle abc is - Maths - Triangles

Question

in a triangle abc ,the bisector of angle abc and angle acb meet at
o,if ob=oc,rove that triangle abc is an isosceles triangle

Neha Sethi · Accepted Answer

Dear student
We draw the figure from the given information which is as
below:
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5b3e325c079a0%20png">
Given:  OB=OCOB  is the bisector of ∠B⇒∠ABO=∠OBC=12∠BOC  is the bisector of ∠C⇒∠ACO=∠OCB=12∠CNow, OB=OC⇒∠OBC=∠OCB   angles opposite to equal sides are equal
⇒2∠OBC=2∠OCB⇒∠ABC=∠ACB⇒AB=AC  sides oppposite to equal angles are equal

in a triangle abc ,the bisector of angle abc and angle acb meet at o,if ob=oc,rove that triangle abc is an isosceles triangle