Chapter 2.6, Problem 21WE

To determine

To prove: $\angle 3\cong \angle 2$ using two column method

Explanation of Solution

Given:

The given figure is,

  

  $\overrightarrow{AB}\perp \overrightarrow{BC}$ and $\angle 3$ is comp to $\angle 1$

Statement	Reason
$\overrightarrow{AB}\perp \overrightarrow{BC}$ and $\angle 3$ is comp to $\angle 1$	Given
$m\angle 3+m\angle 1={90}^0$	$\angle 3$ is comp to $\angle 1$
$m\angle 1+m\angle 2={90}^0$	$\overrightarrow{AB}\perp \overrightarrow{BC}$
$\angle 3+\angle 1=\angle 1=\angle 2$	Both are equal to 90 degrees
$m\angle 3=m\angle 2$	Simplification
$\angle 3\cong \angle 2$	Equal angles are congruent