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Solution :

Given :In trapezium □ABCD, AB ∥ CD.Diagonals AC, BD intersect at O.

R.T.P :

Construction : Draw a line EF passing through the point 'O' and parallel to CD and AB.

Proof :In ∆ACD, EO || CD

∴

.....(1)

[∵ line drawn parallel to one side of a triangle divides other two sides in the same ratio by Basic proportionality theorem]

In ∆ABD, EO ∥ AB

Hence,

[∵ Basic proportionality theorem]

.....(2) [∵ Invertendo]

From (1) and (2),

⇒

[∵ Alternendo]

(Q24) ABCD is a trapezium in which AB ∥ DC and its diagonals intersect each other at point 'O'. Show that AO BO = CO DO .