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Point M and N are taken on the diagonal AC of a parallelogram ABCD such that AM-CN. Prove that BMDN is a parallelogranı.A- |
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Answer» Solution :Given,ABCD is aParallelogram. M and N are points taken on the diagonal AC such that AM = CN.Proof:-We know that the diagonals of a Parallelogram bisect each other. Therefore Ac and BD bisect each other at O.∴ OC= OABut CN = AM∴ OC - CN = OA - AM⇒ OM = ONThus, in quadrilateral BMDN diagonals BD and MN are such that OM = ON and OD = OB,i.e., the diagonal BD and MN bisect each other.Hence, BMDN is a parallelogram. |
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