Question

ABCD is a trapezium having AB || DC. Prove that O, the point of intersection of diagonals, divides the two diagonals in the same ratio. Also prove that $\frac{\mathrm{ar}\left(∆\mathrm{OCD}\right)}{\mathrm{ar}\left(∆\mathrm{OAB}\right)}=\frac{1}{9}$, if AB = 3 CD.

Answer 1

We are given ABCD is a trapezium with AB||DC

Consider the triangles AOB and COD in which

Therefore,

Hence we have proved that O, the point of intersection of diagonals, divides the two diagonals in the same ratio.

We are given AB = 3CD and we have to prove that

We already have proved that AOB and COD are similar triangles

So

Hence, Prove that