Question

abcd is a trapezium in which AB parallel ti dc and its diagonals intersect​

Answer 1

Given parameters

ABCD is a trapezium where AB || DC and diagonals AC and BD intersect at O.

To prove

AOBO=CODO

Construction

Draw a line EF passing through O and also parallel to AB

Now, AB ll CD

By construction EF ll AB

∴ EF ll CD

Consider the ΔADC,

Where EO ll AB

According to basic proportionality theorem

AEED=AOOC ………………………………(1)

Now consider Δ ABD

where EO ll AB

According to basic proportionality theorem

AEED=BOOD ……………………………..(2)

From equation (1) and (2) we have

AOOC=BOOD

⇒ AOBO=OCOD

Hence proved .

its the answer....