Question 6 : 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.
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Step-by-step explanation:
Given AB and CD are straight lines which intersect at O. OP is the bisector of ∠AO.
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 rate opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle. Similarly, the bisection of ∠AOD also bisects the ∠BOC.
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