ABCD is a trapezium in which AB||DC and its diagonals intersect each other at point ‘O’. Show that

Given, ABCD is a trapezium where AB||DC

And diagonals intersect at each other ‘O’.

Need to prove

⇒ Let us draw a line EF||DC passing through point O.

⇒ Now, in ADC, EO || DC

(because EF || DC)

So, …………………eq (1)

Now, Line drawn parallel to one side of a triangle intersects the other two sides in distinct points, and then it divides the other 2 sides.

Similarly, in DBA, EO || AB

(Because EF || AB)

⇒ …………………..eq(2)

⇒ From eq(1) and eq(2)

⇒

⇒

Hence Proved.