Final answer:
The bases of a cylinder are perpendicular to the axis of the cylinder, and any line joining corresponding points on the cylinder's bases will be perpendicular to those bases.
Step-by-step explanation:
The bases of a cylinder are perpendicular to the line joining corresponding points of the bases because a cylinder is a three-dimensional geometrical shape whose side surfaces are formed by extending lines that are perpendicular to the circular bases. This perpendicular relationship is based on the definition and geometric construction of a cylinder. The line segments joining corresponding points on the bases are parallel to the axis of the cylinder and hence are perpendicular to the bases.
In a coordinate system with the origin at the center of the cylinder, you can visualize this by considering the cylindrical axis as the z-axis. Then, the bases sit parallel to the x-y plane, and the perpendicular lines joining points on the bases would extend along the z-axis. This alignment emphasizes the 90-degree angle between the base planes and the lines extending perpendicular to them, which are radial lines from the axis.
An example to visualize is thinking of the cylinder as being similar to a canned food item. If we were to draw a straight line from the center of the top lid directly down to the center of the bottom lid, this line would be the axis of the cylinder and would be perpendicular to both lids (bases). If we draw another line from any point on the edge of the top lid to the corresponding point directly below it on the bottom lid, this line would also be perfectly vertical and perpendicular to both lids.