Exercise 4 Page 374

We are asked to describe the relationship between the measures of angles formed when two parallel lines are cut by a transversal. Let's start with a graph. We can see that when a pair of lines is cut by a transversal, eight different angles are created. The eight angles formed by the lines and the transversal receive special names.

Name	Description
Alternate Interior Angles	Angles that lie between the lines on opposite sides of the transversal.
Alternate Exterior Angles	Angles that lie outside the lines on opposite sides of the transversal.
Corresponding Angles	Angles that lie in the same position in relation to the transversal.

If we take a look at the graph, we will see that there are exactly two pairs of angles that lie between the lines on opposite sides of the transversal — alternate interior angles.

Name	Description	Angles
Alternate Interior Angles	Angles that lie between the lines on opposite sides of the transversal.	$\angle 3$ and $\angle 5,$ $\angle 4$ and $\angle 6$
Alternate Exterior Angles	Angles that lie outside the lines on opposite sides of the transversal.
Corresponding Angles	Angles that lie in the same position in relation to the transversal.

Also, there are two pairs of alternate exterior angles.

Name	Description	Angles
Alternate Interior Angles	Angles that lie between the lines on opposite sides of the transversal.	$\angle 3$ and $\angle 5,$ $\angle 4$ and $\angle 6$
Alternate Exterior Angles	Angles that lie outside the lines on opposite sides of the transversal.	$\angle 1$ and $\angle 7,$ $\angle 2$ and $\angle 8$
Corresponding Angles	Angles that lie in the same position in relation to the transversal.

Last, there are four pairs of corresponding angles. These are the angles that lie in the same position around the intersection points.

Name	Description	Angles
Alternate Interior Angles	Angles that lie between the lines on opposite sides of the transversal.	$\angle 3$ and $\angle 5,$ $\angle 4$ and $\angle 6$
Alternate Exterior Angles	Angles that lie outside the lines on opposite sides of the transversal.	$\angle 1$ and $\angle 7,$ $\angle 2$ and $\angle 8$
Corresponding Angles	Angles that lie in the same position in relation to the transversal.	$\angle 1$ and $\angle 5,$ $\angle 2$ and $\angle 6,$ $\angle 3$ and $\angle 7,$ $\angle 4$ and $\angle 8$

Now, note that the angle measures in each pair are related. Because we are told that the lines are parallel, the angles in each pair have the same measure.