Question

In a quadrilateral TRUE, diagonals TU and RE are perpendicular bisectors of each other. Quadrilateral TRUE must be a?

1) Rectangle
2) Rhombus
3) Square
4) I, II and III

Answer 1

In a quadrilateral with diagonals that are perpendicular bisectors of each other, the shape must be a square, which is both a rectangle and a rhombus.

Step-by-step explanation:

In a quadrilateral TRUE, if diagonals TU and RE are perpendicular bisectors of each other, this means that each diagonal cuts the other into two equal lengths and they intersect at a 90-degree angle. This property indicates that quadrilateral TRUE is both a rhombus (since all sides are equal as the diagonals bisect each other) and a rectangle (since the diagonals are perpendicular, so all angles are 90 degrees). Therefore the quadrilateral must be a square, which is both a rectangle and a rhombus. Hence, the correct answer is a square.