**Theorem 1.16**: If a line is perpendicular to one of
two perpendicular lines it is parallel to the other.

**Proof**: If the given line is perpendicular to the
first line, its slope is the negative reciprocal of the slope of that line. If
that line is perpendicular to the other line, its slope is the
negative reciprocal of that of the other line. Conclude that the
slope of the given line is the negative reciprocal of the negative
reciprocal of the other line. However, the negative reciprocal of the
negative reciprocal of a number is the same as the original number,
and we conclude that the given line has the same slope as the other line, and is hence parallel
to it.