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In following figure , PS is the bisector of LQPR and PTLQR. Showthat <TPS = ½(ZQ-2R) |
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Answer» Given; PS is bisector of angle QPR PT is perpendicular to QR To Prove; angle TPS = 1/2 (angle Q - angle R) Solutio; We know that angle QPS = 1/2 angle P(1) angle Q + angle QPT = 90 degreeangle QPT = 90 degree -angle Q (2) On putting equations (1) and (2) angle TPS = angle QPS - angle QPT= 1/2 angle P - ( 90 - angle Q )= 1/2 angle P - 90 + angle Q = 1/2 angle P - 1/2 (angle Q + angle P + angle R) + angle Q= 1/2 angle P - 1/2 angle Q - 1/2 angle P - 1/2 angle R + angle Q = -1/2 angle Q - 1/2 angle R + angle Q (+ve and -ve 1/2 angle P got cancled ) by takig LCM in angle Q we get -1/2 angle Q + 2/2 angle Q - 1/2 angle R (-1/2 + 2/2) angle Q - 1/2 angle R = 1/2 angle Q - 1/2 angle R angle TPS = 1/2 ( angle Q -1/2 angle R ) (Hence proved) |
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