**Theorem 1.13**: A
line is
parallel to one of two
parallel
lines if and only if it is
parallel to the other.

**Proof**: If a line
is parallel to one of
two parallel
lines, then they all have
the same slope, and are
all parallel to each
other.

If it is not parallel to one of two parallel lines then it has a different slope from the one parallel line and so has a different slope than the other of the two parallel lines, and is not parallel to the other line either.