Question

in an isosceles triangle ABC with AB = AC, THE BISECTOR 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

Answer:

,

Step-by-step explanation:

OB=OA

given :-

AB=AC. (1)

OB IS THE BISECTOR OG ANGLE B

SO, ANGLE ABO=ANGLE OBC=1/2 ANGLE B. (2)

OC IS THE BISECTOR OF ANGLE C

SO, ANGLE AOC =ANGLE OCB=1/2ANGLE C. (3)

TO PROVE:- OB=OC

PROOF:

SINCE, AB=AC

Angle ACB=Angle abc (angle opposite to equal sides are equal)

1/2 angle aACB=1/2angleABC

Angle OCB=angle OBC ( from (1) and (2))

Hence, OB=oc ( sides opposite to equal angles are equal)

Hence proved

AO bisect angle A

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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