If one diagonal of a trapezium divides the other

Asked by admin @ 17/08/2021 in Math viewed by 230 People

. 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.

Answered by admin @ 17/08/2021

Given that the diagonal BD the diagonal AC in AO : OC in 3 : 1
To prove : AB = 3CD
Proof : in Δ AOC and Δ DOC
Δ AOB = Δ COD
Δ OBA = Δ ODC (Because DC is parallel to AB, and DB is transversal so these are alternates)
Therefore,
Δ AOB is similar to COD (By AA similarity)
Now, AO/OC = AB/DC (Because in similar triangles sides are proportional)
3/1 = AB/DC (Given that AO : OC = 3 : 1)
So, AB = 3DC
Hence proved.

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If one diagonal of a trapezium divides the other

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