ABCD is trapezium with ab parallel dc
Answers
Answer:
ABCD is trapezium with ab parallel dc
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 the basic proportionality theorem
AE/ED=
AO/OC
………………………………(1)
Now consider Δ ABD
where EO ll AB
According to the basic proportionality theorem
DE/EA = DO/BO…………….(ii)
From equation (i) and (ii), we get,
AO/CO = BO/DO
⇒AO/BO = CO/DO
Hence, proved.
Hence the proof.
Step-by-step explanation:
Given parameters
ABCD is a trapezium where AB || DC and diagonals AC and BD intersect at O.
To prove
A
O
B
O
=
C
O
D
O
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 the basic proportionality theorem
A
E
E
D
=
A
O
O
C
………………………………(1)
Now consider Δ ABD
where EO ll AB
According to the basic proportionality theorem
DE/EA = DO/BO…………….(ii)
From equation (i) and (ii), we get,
AO/CO = BO/DO
⇒AO/BO = CO/DO
Hence, proved.
Hence the proof.
