Q. 35.0( 1 Vote )

In m ABCD, M is the mid-point of . and intersect in N. Prove that DN = 2MN.

Answer :

In ABCD, M is the mid-point of. and intersect in N.



To prove : DN = 2MN


Proof: M is the mid-point of BC


MB = MC


…(1)


In ∆MBN and ∆MCD


BMN CMD (Vertically opposite angles)


MNB MDC (Alternate angles)


The correspondence MBNMCD is a similarity



(from 1)


MN = MD


Now, D-M-N


DN = DM + MN


DN = DM + MN


DN = MN + MN (MD = MN)


DN = 2MN


Hence proved.


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