Question

The diagonals of a quadrilateral ABCD intersect each other at the point O, and it is given that (AO)/(BO) = (CO)/(DO). What can you conclude about quadrilateral ABCD?

A) ABCD is a parallelogram.
B) ABCD is a rhombus.
C) ABCD is a trapezium.
D) ABCD is a rectangle.

Answer 1

The given condition suggests that the quadrilateral ABCD is a parallelogram.

Step-by-step explanation:

The given condition (AO)/(BO) = (CO)/(DO) tells us that the ratio of the lengths of the segments AO and BO is equal to the ratio of the lengths of the segments CO and DO. This means that the diagonals AO and BO are divided into the same proportions as the diagonals CO and DO. In a parallelogram, the diagonals bisect each other, meaning they divide each other into equal lengths. Therefore, the fact that the diagonals of ABCD are divided into the same proportions suggests that ABCD is a parallelogram.