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ICSE Class 9 Answered

In triangle ABC the bisector of angle ABC and ACB meet at O.If OB=OC prove that triangle ABC is an isosceles triangle.
Asked by rkarim957 | 14 Jul, 2019, 11:53: AM
answered-by-expert Expert Answer
Given : Triangle OBC is an isosceles triangle. BO and CO are the bisectors of angle B and angle C.
To prove : triangle ABC is an isosceles
Proof :
In triangle OBC,
OB = OC
angle OBC = angle OCB                opposite angles of equal sides
angle AOB = angle OBC .....(i)
and angle ACO = angle OCB ....(ii)
Adding (i) and (ii) we get
angle AOB + angle ACO = angle OBC +  angle OCB
angle ABC = angle ACB
AB = AC                                     opposite sides of an equal angles
Hence, triangle ABC is an isosceles triangle.
 
Answered by Sneha shidid | 15 Jul, 2019, 10:14: AM

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