Q10 of 65 Page 128

The diagonals of a quadrilateral ABCD intersect each other at the point O such thatShow that ABCD is a trapezium

Draw a line OE parallel to AB


Given: In triangle ABD, OE is parallel to AB


Now, using basic proportionality theorem, we obtain


(i)


It is given that,


(ii)


From (i) and (ii), we get



EO || DC (By the converse of basic proportionality theorem)


⇒ AB || OE || DC


⇒ AB || CD


Hence,


ABCD is a trapezium


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