Yes. It is a theorem. To prove it, use contradiction.
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I line that intersects a segment at its midpoint.
The midpoint of a line segment would be to add up all of the numbers in the segment. Then divide by the number of numbers that were added. For example if a 1, 3, and 8 were added, divide by 3. This will give the midpoint of the line segment.
It's called a perpendicular bisector of the line segment.
It is perpendicular line segment
A line segment cannot have more than one midpoint or else you will be creating multiple line segments that are connected to each other. A line segment can only have one midpoint.