Prove that the bisectors of a …

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Prove that the bisectors of a pair of vertically opposite Angles are in the same straight line.

Posted by Nidhi Jain 5 years ago

CBSE > Class 09 > Mathematics

1 answers

Aryan Kumar 5 years ago

AB and CD are straight lines intersecting at O. OX the bisector of angles ∠AOC and OY is the OY is the bisector of ∠BOD. OY is the bisector of ∠BOD. ∴ ∠1 = ∠6 … (1) OX is the bisector of ∠AOC. ∴ ∠3 = ∠4 … (2) ∠2 = ∠5 … (3) (Vertically opposite angles) We know that, the sum of the angles formed at a point is 360°. ∴ ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 = 360° ⇒ ∠1 + ∠2 + ∠3 + ∠3 + ∠2 + ∠1 = 360° (Using (1), (2) and (3)) ⇒ 2∠1 + 2∠2 + 2∠3 = 360° ⇒ 2(∠1 + ∠2 + ∠3) = 360° ⇒ ∠DOY + ∠AOD + ∠AOX = 180° ⇒ ∠XOY = 180° ∴ The bisectors of pair of vertically opposite angles are on the same straight line.

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CBSE > Class 09 > Mathematics