09. ABCD is a trapezium in which AB || DC and itsdiagonals intersect e

1.	09. ABCD is a trapezium in which AB \|\| DC and itsdiagonals intersect each other at the point O. ShowAO COBO DOthat
Answer» Given: ABCD is a trapezium where, AB ll CDDiagonals 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 CDConsider the ΔADC,EO ll DCThus, 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) Like my answer if you find it useful!

09. ABCD is a trapezium in which AB || DC and itsdiagonals intersect each other at the point O. ShowAO COBO DOthat

Answer»

Given: ABCD is a trapezium where, AB ll CDDiagonals 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 CDConsider the ΔADC,EO ll DCThus, 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)

Like my answer if you find it useful!

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