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
Answers
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:
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.