Q. 175.0( 9 Votes )

Prove that the li

Answer :


Let ABCD be a trapezium in which AB||DC and let M and N be the mid-points of the diagonals AC and BD, respectively.


Now, join CN and produce it to AB at E.


In ΔCDN and ΔEBN, we have,


DN = BN


DCN = BEN


CDN = EBN


ΔCDN EBN


DC = EB and CN = NE


Thus, in ΔCAE, the points M and N are the mid-points of AC and CE, respectively.


MN||AE


MN||AB||CD


Hence, proved.


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