Question

8. ABCD is a trapezium in which AB||DC and its diagonals intersect each other at point ‘O'.
show that
AO/BO= CO/DO

​

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

AE upon ED=AO upon OC ………………………………(1)

Now consider Δ ABD

where EO ll AB

According to basic proportionality theorem

AE upon ED=BO upon OD ……………………………..(2)

From equation (1) and (2) we have

AO upon OC=BO upon OD

⇒ AO upon BO=OC upon OD

Hence the proof.

$\huge\mathbb{\purple{ハンはジャクソンが大好き}}$