Question

9. ABCD is a trapezium in which AB || DC and its
diagonals intersect each other at the point O. Show
Q
AO
CO
that
BO DO​

Answer 1

Step-by-step explanation:

ABCD is a trapezium in which AB parallel DC and its diagonals intersect each other at point O . show that AO/BO = CO/DO. ABCD is a trapezium where AB || DC and diagonals AC and BD intersect at O. Hence the proof.

Answer 2

Answer:

Given parameters

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

To prove

AO/BO=CO/DO

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/ED=AO/OC ………………………………(1)

Now consider Δ ABD

where EO ll AB

According to basic proportionality theorem

AE/ED=BO/OD ……………………………..(2)

From equation (1) and (2) we have

AO/OC=BO/OD

⇒ AO/BO=OC/OD

Hence the proof.