Chapter 3.6, Problem 30PPS

To determine

To Prove: $l\parallel m$

Explanation of Solution

Given: $l$ is equidistant from $n$ and $m$ is equidistant from $n$ .

  

We know that if two lines are equidistant, they are parallel.

Thus

  $l\parallel mandm\parallel n$

Since slopes of parallel lines are equal.

Thus

  $\begin{array}{l}slopeofl=slopeofn\\ slopeofm=slopeofn\end{array}$

Using the transitive property, it is concluded that

  $l\parallel m$

Hence proved.