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If two straight lines intersect each …

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If two straight lines intersect each other then prove that the ray opposite to the bisector of one of the angels so formed bisects the vertically opposite angle.

Posted by Md Kaif 3 years, 11 months ago

CBSE > Class 09 > Mathematics

1 answers

Manaswini ??? 3 years, 11 months ago

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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