Chapter 3.3, Problem 22WE

To determine

To prove: the theorem in two columns method.

Explanation of Solution

Given information:

Given figure:

  

Calculation:

Consider the theorem, If a transversal intersecting two lines making a pair of same side interior angle supplementary, then the two lines are parallel.

In figure transversal $t$ cut line $k$ and line $n$ respectively.

Two column form proof is as follows:

Statements	Reasons
$\angle 2$ and $\angle 1$ are supplementary	Given
$\angle 2+\angle 3=180°$	Angle addition postulate
$\angle 2$ and $\angle 3$ are also supplementary	Definition of supplementary angle
$\angle 1\cong \angle 3$	Two angle supplementary to same angle are congruent
$k\parallel n$	Alternate angle theorem