Answer :

Given: ABCD is a trapezium with AB || CD and the diagonals AC and BD intersect at 'O'.

To prove: =

Proof:

In the figure consider the triangle OAB and OCD

∠DOC = ∠ΑOB (Vertically opposite angles are equal)

since AB || DC,

∠DCO = ∠OAB (Alternate angles are equal)

∴ By AA corollary of similar triangles.

∴ Δ OAB ∼ Δ OCB When the two triangle are similar, the side are proportionally.

⇒ =

Cross-multiplying, we get,

Hence proved.

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