Answer :

__Given:__ BD divides the diagonal AC in ratio 1:2

__To Prove:__ DC = 2 AB

__Proof:__

In, ΔAOB and ΔCOD

∠ OAB = ∠ OCD [ Alternate angles are equal as AB || CD]

∠ABO = ∠ ODC [Alternate angles are equal as AB || CD]

Therefore, Δ AOB ≈ Δ COD By AAA Similarity

Now as both the triangles are similar we can say that,

As

[ Given]

We can say that

And therefore by cross multiplying, CD = 2 AB

Hence, Proved.

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