Math, asked by narendermodi4737, 1 year ago

Abcd is a trapezium in which ab parallel to dc and its diaginals intersect each other at o. Prove that AO by BO equal to CO by DO

Answers

Answered by smartcow1
25
Hey there,

Given: □ABCD is a trapezium where, AB ll CD
Diagonals AC and BD intersect at point O.

Construction: Draw a line EF passing through O and also parallel to AB.

Now, AB ll CD, since by construction, EF ll AB ⇒ EF ll CD
Consider the ΔADC,
EO ll DC
Thus, by Basic proportionality theorem, (AE / ED) = (AO / OC) .... (i)
Now, consider Δ ABD,
EO ll AB,
Thus, by Basic proportionality theorem, (AE / ED) = (BO / OD) .... (ii)
From (i) and (ii), we have, (AO / OC) = (BO / OD) (since L.H.S of i and ii are equal)
Hence we proved that, (AO / OC) = (BO / OD)

Hope this helps!
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