Math, asked by vi9pata5saipra, 1 year ago

If two straight lines intersect each other,prove that the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.

Answers

Answered by Golda
608
Given AB and CD are straight lines which intersect at O. OP is the bisector of ∠ AOC.
To prove : OQ is the bisector of ∠ BOD
Proof :
AB, CD and PQ are straight lines which intersect in O.
∠ AOP = ∠ BOQ (vertically opposite angles)
∠ COP = ∠ DOQ (vertically opposite angles)
∠ AOP = ∠ COP (OP is the bisector of ∠ AOC)
∴ ∠ BOQ = ∠ DOQ
Thus, the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.
Similarly, the bisector of ∠ AOD also bisects the ∠ BOC.

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Answered by pbsb2005
27

Answer:

attached pic is the answer

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