ABCD IS A TRAPEZIUM IS WHICH AB||DC AND ITS DIAGONALS INTERSECT EACH OTHER AT THE POINT O SHOW THAT
AO|BO
=
CO|DO
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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 the proof.
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