Q. 45.0( 7 Votes )

If one diagonal of a trapezium divides the other diagonal in the ratio 1 : 3. Prove that one of the parallel sides is three times the other.

Answer :



Given: BD divides the diagonal AC in ratio 1:3


To Prove: DC = 3 AB


Proof:


In, Δ AOB and Δ COD


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


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


Therefore, Δ AOB ≈ Δ COD By AA Similarity


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



As


[ Given]


We can say that



And therefore by cross multiplying, CD = 3 AB


Hence, Proved.


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