Florida Teacher Certification Examinations (FTCE) Subject Area Practice Test

In a quadrilateral where the diagonals are congruent perpendicular bisectors of each other, what polygon is identified?

1. Rectangle

2. Square

3. Rhombus

4. Parallelogram

The correct answer is: Square

In a quadrilateral where the diagonals are congruent and also serve as perpendicular bisectors of each other, the specific polygon identified is a square. This is due to several defining properties of a square: not only are the diagonals equal in length, but they also intersect at right angles and bisect each other at their midpoints. These conditions are met uniquely by a square among the quadrilaterals. While a rectangle has congruent diagonals, it does not necessarily have perpendicular diagonals unless it is a square. A rhombus has diagonals that are perpendicular and bisect each other but does not require the diagonals to be congruent. Lastly, a parallelogram has diagonals that bisect each other, but like the rectangle and rhombus, it does not meet the conditions of having both congruent and perpendicular diagonals unless it is specifically a square. Thus, the uniqueness of these diagonal properties in the context of the quadrilateral leads to the conclusion that a square is the correct identification for the polygon.