Answer :

The quadrilateral ABCD is shown below, BD and AC are the diagonals.

**Construction:**Draw a line OE parallel to AB

**Given: **In ΔABD, OE is parallel to AB

**To prove :**ABCD is a trapezium

According to basic proportionality theorem, if in a triangle another line is drawn parallel to any side of triangle,

then the sides so obtain are proportional to each other.

Now, using basic proportionality theorem in ΔDOE and ΔABD, we obtain

...(i)

It is given that,

...(ii)

From (i) and (ii), we get

...(iii)**Now for ABCD to be a trapezium AB has to be parallel of CD**

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

Now if,⇒ AB || OE || DC

Then it is clear that⇒ AB || CD

Thus the opposite sides are parallel and therefore it is a trapezium.Hence,

ABCD is a trapezium

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