36. Rectangle ABCD is shown in the figure. If ABCD is not a square, which of the following is a pair of perpendicular line segments?
Answer: D
AB and BC are a pair of perpendicular line segments.
In rectangle ABCD, the sides AB and BC form a right angle at point B, making them perpendicular to each other.
A) AB and DC
AB and DC are opposite sides of the rectangle and are parallel to each other. Therefore, they cannot be perpendicular as perpendicular lines intersect at a right angle.
B) AD and BD
AD is a vertical side of the rectangle, while BD is a diagonal line segment. Diagonal lines do not form perpendicular angles with the sides of the rectangle unless in the case of a square, which is not applicable here.
C) AC and BD
AC is a diagonal of the rectangle and BD is another diagonal. While they may intersect, they do not form a right angle at their intersection point, thus they are not perpendicular.
D) AB and BC
AB and BC are adjacent sides of the rectangle, meeting at vertex B, which creates a right angle. This confirms that they are indeed perpendicular to each other.
Conclusion
The only pair of segments that are perpendicular is AB and BC, as they intersect at a right angle. All other options either consist of parallel lines or do not form a right angle, making them incorrect choices. Thus, option D is definitively the correct answer.