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 MBN↔MCD 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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