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the diagonals of quadrilateral ABCD intersect each other at the point O such that AO/BO = CO/DO. show that ABCD is a trapezium. |
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Answer» Answer: given:AO/BO=CO/DO to proove: ABCD is a trapezium Step-by-step explanation: PROOF: AO/BO=CO/DO (given) cross multiplying, AO/CO=BO/DO in triangle AOB and triangle COD, AO/CO=BO/DO (prooved above) angleAOB=angleCOD (VERTICALLY opposite angles) Therefore,. angleCDO= angleABO ( CPST) But angleCDO and angleABO are ALTERNATE angles. Hence,AB is parallel to CD and therefore,ABCD is a trapezium. Hope it helps. |
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