Question

In an isosceles triangle ABC, with AB=AC, the bisectors of angle B and angle C intersect each other at O. Join A to O show that OB=OC and AO bisects angle A

Answer 1

Given: in an isosceles triangle ABC, bisecrors of B and C intersect at O. join A to O.
To Prove: OB= OC
AO BISECTS <A
PROOF: in triangle AOB AND AOC
AB = AC ( GIVEN)
< ABO = < ACO ( O bisects < B and<C)
AO = AO( COMMON)
》triangle AOB is congruent to AOC
( by SAS rule)
OB = OC ( BY CPCT)

< OAB = < OAC( BY CPCT)
》 AO bisects < A
Hence proved

Answer 2

Step-by-step explanation:

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Solution:-

Solution:-Given:-

AB = AC and

the bisectors of B and C intersect each other at O

(i) Since ABC is an isosceles with AB = AC,

B = C

½ B = ½ C

⇒ OBC = OCB (Angle bisectors)

∴ OB = OC (Side opposite to the equal angles are equal.)

(ii) In ΔAOB and ΔAOC,

AB = AC (Given in the question)

AO = AO (Common arm)

OB = OC (As Proved Already)

So, ΔAOB ΔAOC by SSS congruence condition.

BAO = CAO (by CPCT)

Thus, AO bisects A.

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