Question

if only diagonal of a trepezium divides the other diagonal in the ratio 1:3 prove that one of the parallel side is three times the other​

Answer 1

Answer:

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.

Step-by-step explanation:

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