Chapter 2.6, Problem 20WE

To determine

To prove: $\angle 3\cong \angle 4$ using two column method.

Explanation of Solution

Given:

The given figure is,

  

And the condition is,

  $\angle 3$ is supplementary to angle $\angle 1$ and

  $\angle 4$ is supplementary to angle $\angle 2$

Steps:	Reason:
$m\angle 3+m\angle 1=180$	$\angle 3$ is supplementary to angle $\angle 1$
$m\angle 4+m\angle 2=180$	$\angle 4$ is supplementary to angle $\angle 2$
$m\angle 1=m\angle 2$	Alternate opposite angle
$m\angle 3+m\angle 1=m\angle 4+m\angle 2$	Since both are equal to 180
$m\angle 3=m\angle 4$	Since, $m\angle 1=m\angle 2$
$\angle 3\cong \angle 4$	Since, equal angles are congruent