If two straight lines intersect each other then prove that the ray opposite to the bisector of one of the angles so formed bisects the vertically opposite angle.
Given, lines AB and CD intersect each other at point O.
OE is the bisector of ∠ BOD.
TO prove: OF bisects ∠AOC.
Proof:
AB and CD intersect each other at point O.
Therefore, ∠ AOC = ∠ BOD
∠ 1 = ∠ 2 [OE is the bisector of ∠BOD] _________________ (i)
∠ 1 = ∠ 3 and ∠ 2 = ∠ 4 [Opposite angles] ____________ (ii)
From equations (i) and (ii)
∠ 3 = ∠ 4
Hence, OF is the bisector of ∠AOC.
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