Exercise 16 Page 525

Let's take a look at the diagram we have been given.

Examining the diagram, we see that $\angle ABC$ is a right angle. We also see that $\angle ABC$ equals the sum of $\angle 1$ and $\angle 2.$ Therefore, by the Angle Addition Postulate we can write the following equation. Using the Substitution Property of Equality, we can prove that the sum of $m\angle 1$ and $m\angle 2$ equals $90^{\circ }.$ Since the sum of $\angle 1$ and $\angle 2$ equals $90^{\circ },$ we know that these angles are complementary. Let's show this as a two-column proof.

Statement	Reason
$\overrightarrow{BA}\perp \overrightarrow{BC}$	Given
$\angle ABC$ is a right angle	Definition of perpendicular lines
$m\angle ABC=90^{\circ }$	Definition of a right angle
$m\angle 1+m\angle 2=m\angle ABC$	Angle Addition Postulate
$m\angle 1+m\angle 2=90^{\circ }$	Substitution Property of Equality
$\angle 1$ and $\angle 2$ are complementary	Definition of complementary angles