Final answer:
In geometry, when two lines are both perpendicular to a third line, they are parallel to each other because they maintain a constant distance and do not intersect.
Step-by-step explanation:
The student's question relates to the concept of lines in a plane in geometry which is a part of Mathematics. Specifically, the scenario described involves three lines that are coplanar; two of which are perpendicular to the third line. According to the principles of geometry, if two lines are both perpendicular to a third line, they must be parallel to each other. This is because two lines perpendicular to the same line cannot intersect each other and must maintain a constant distance apart, which is the definition of parallel lines.
An example to visualize this concept is the three-dimensional Cartesian coordinate system, where the x-axis, y-axis, and z-axis are all mutually perpendicular to each other. If we take any two axes, for instance, the x-axis and y-axis, they are both perpendicular to the z-axis, which means they are parallel in the xy-plane. Likewise, in this student's case, the two lines that are perpendicular to the third are parallel to each other in their plane.