Why two lines, perpendicular to the third, do not intersect?

If we assume that a straight line that is perpendicular to the other two is a secant, then we can use theorems on the parallelism of straight lines.
Theorem: If the corresponding angles are equal, then the lines are parallel.
1. Since the secant is perpendicular to the straight lines, the angle between the straight line and the secant is 90 °.
2. Since the angle between the secant and the first line is 90 °, and the angle between the secant and the second line is also 90 °, therefore the corresponding angles are equal.
3. If the corresponding angles are equal, therefore, the straight lines are parallel.