Schoolcrop

Solution :

Given : □ABCD, AB ∥ DC

The diagonals AC and BD intersect at 'O'.

R.T.P :

Construction : Draw EF || AB, passing through 'O'.

Proof : In ∆ACD, OE ∥ CD [∵ Construction]

Hence,

.....(1)

(∵ Line drawn parallel to one side of a triangle divides other two sides in the same ratio - Basic proportionality theorem)

Also in ∆ABD, EO ∥ AB [Construction]

Hence,

.....(2)

(∵ Basic proportionality theorem) From (1) and (2), we have

∴ Hence Proved

(Q25) Diagonals AC and BD of a trapezium ABCD with AB ∥ DC intersect each other at the point 'O'. Using the criterion of similarity for two triangles, show that OA OC = OB OD