Question

if one diagonal of a Trapezium divides the other diagonal in 1 is to 2 ratio prove that one of the parallel sides is double the other​

Answer 1

Step-by-step explanation:

See the attachment please...

Answer 2

Step-by-step explanation:

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.