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Prove that the bisectors of a pair of vertically opposite angles are in the same straight line. |
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Answer» 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 360ï½.∴ 1 + 2 + 3 + 4 + 5 + 6 = 360ï½⇒ 1 + 2 + 3 + 3 + 2 + 1 = 360ï½ (Using (1), (2) and (3))⇒ 21 + 22 + 23 = 360ï½⇒ 2(1 + 2 + 3) = 360ï½⇒ DOY + AOD + AOX = 180ï½⇒ XOY = 180ï½∴ The bisectors of pair of vertically opposite angles are on the same straight line.HOPE IT HELPS..! |
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