Rectangle ABCD: Are the Diagonals Perpendicular to Each Other?

To determine whether the diagonals of rectangle $ABCD$ are perpendicular, we need to recall the geometric properties of a rectangle. In a rectangle, the diagonals are congruent, which means they have the same length, but they are not inherently perpendicular. An exception occurs only if the rectangle is also a square, as squares have perpendicular diagonals.

Let's review the properties:

• Each diagonal divides the rectangle into two congruent right triangles.
• The diagonals of a rectangle are equal in length: $AC = BD$.
• The diagonals are not perpendicular; they do not intersect at right angles unless the rectangle is a square.

Since there is no information provided that suggests rectangle $ABCD$ is a square, we conclude based on standard rectangle properties that the diagonals $AC$ and $BD$ are not perpendicular.

Thus, the statement "The diagonals of rectangle $ABCD$ are perpendicular to each other" is False.