FTCE Professional Education Practice Exam

What is true about the diagonals of a rectangle?

1. They are congruent and bisect each other

2. They are always unequal

3. They do not bisect each other

4. They are perpendicular

The correct answer is: They are congruent and bisect each other

The statement that the diagonals of a rectangle are congruent and bisect each other is indeed true. In a rectangle, both diagonals are of equal length due to the equal lengths of opposite sides and the properties of congruent triangles formed by drawing the diagonals. When the diagonals intersect, they divide each other into two equal parts, which is a defining characteristic of rectangles. This property is inherent in all parallelograms, of which rectangles are a specific type. The length congruence of the diagonals can be confirmed using the Pythagorean theorem, as each diagonal can be considered the hypotenuse of triangles formed by the rectangle's sides. Additionally, the fact that these diagonals bisect each other demonstrates that rectangles maintain symmetry along both their diagonals. In summary, the correct answer highlights fundamental properties of rectangles, which are crucial for understanding their geometric characteristics.