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

Question

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

Philoid · Accepted Answer

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