Q. 24.0( 2 Votes )
If one diagonal of a trapezium divides the other diagonal in the ratio 1:2. Prove that one of the parallel sides is double the other.
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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