Perpendicular Lines
The following theorems characterize parallel lines cut by a perpendicular line:
Theorem. On a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
In the figure above, line r is perpendicular to lines s and t.
Theorem. On a plane, two lines are parallel if and only if they are both perpendicular to the same line.
Prove these theorems as an exercise.
