Chapter 3.3, Problem 20CE

To determine

To prove: $l\parallel n$

Explanation of Solution

Given information: $k\parallel l,k\parallel n$

Formula used: Lines are parallel if and only if corresponding angles are equal.

Proof:

  

As $k\parallel l$ and take $t$ as a transversal,

  $\angle 1=\angle 2$ (if lines are parallel the corresponding angles are equal)

As $k\parallel n$ and take $t$ as a transversal,

  $\angle 1=\angle 3$ (if lines are parallel the corresponding angles are equal)

Use the fact that things which are equal to the same thing are equal to each other.

So,

  $\angle 2=\angle 3$

Hence, $l\parallel n$

(If corresponding angles are equal then lines are parallel)