Question

In the given figure OB, OC are angle bisector of AOC, BOD. Prove that BOD=AOC

Answer 1

we know that the bisectors divide the angle in two equal parts.

so, angle AOC = angle AOB +Angle BOC.

and angle BOD = angle BOC + angle COD.

now, AOB = BOC

And BOC = COD

So, AOB = COD

we had proven that the all given angles are equal then their sum will also be equal.

means, AOB+ BOC = BOC + COD

angle AOC = angle BOD

Hence proved.

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Answer 2

∠AOC = ∠BOD

GIVEN

OB and OC are angle bisector of ∠AOC and ∠BOD respectively.

TO FIND

∠BOD = ∠AOC

SOLUTION

We can simply solve the above problem as follows;

According to angle bisector theorem, an angle bisector is a line segment that divides an angle into two equal parts.

Therefore,

∠AOB = ∠BOC (I)

And,

∠BOC = ∠COD (II)

Also,

∠AOB + ∠BOC = ∠ AOC

And,

∠BOC + ∠COD = ∠BOD

Form (I) & (II)

∠AOB = ∠BOC = ∠COD

Therefore,

∠AOC = ∠BOD

∠AOC = ∠BOD Hence, Proved.

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