False. The statement is false because having all the segments of equal length does not guarantee that a quadrilateral is a rectangle.
To determine if quadrilateral ABCD is a rectangle, we need to consider the properties of a rectangle. A rectangle is a quadrilateral with all angles equal to 90 degrees.
In this case, we are given that the diagonals AC and BD intersect at point O, where AO = BO = CO = DO = 3cm. However, having diagonals of equal length does not necessarily mean that the quadrilateral is a rectangle. There are other quadrilaterals, such as rhombi or squares, that can also have diagonals of equal length but have different angles.
To determine if ABCD is a rectangle, we need additional information, such as the measure of the angles or the relationship between the sides. Without this information, we cannot conclude that ABCD is a rectangle based solely on the given equal lengths of the diagonals.