Question 10:
The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/BO = CO/DO. Show that ABCD is a trapezium.
Answer:
Let us consider the following figure for the given question.
Draw a line OE || AB
In ΔABD, OE || AB
By using basic proportionality theorem, we obtain
AE/ED = BO/OD (1)
However, it is given that
AO/OC = OB/OD (2)
From equation (1) and (2) , we obtain
AE/ED = AO/OC
⇒ EO || DC [By the converse of basic proportionality theorem]
⇒ AB || OE || DC
⇒ AB || CD
∴ ABCD is a trapezium.
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