Chapter 2, Problem 20CR

To determine

To prove: $\angle 3\cong \angle 4$ in two columns method.

Explanation of Solution

Given information:

Given:

  $\angle 3$ is a supplement of $\angle 1$ ;

  $\angle 4$ is a supplement of $\angle 2$ .

Given figure:

  

Calculation:

Consider the figure,

  

Consider the following.

  $\angle 1$ and $\angle 3$ and $\angle 2$ and $\angle 4$ are supplementary

The proof in two column form is as follows:

$\angle 1+\angle 3=180°$	Supplementary angles
$\angle 2+\angle 4=180°$	Supplementary angles
$\angle 1=\angle 2$	Vertically opposite angle
$\angle 1+\angle 4=180°$	$\angle 1=\angle 2$
$\angle 3=\angle 4$	$\angle 1+\angle 4=\angle 1+\angle 3$