Q. 24.0( 2 Votes )

If one diagonal o

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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