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.
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.
Angles that lie in the same position in relation to the transversal.
∠ 1 and ∠ 5, ∠ 2 and ∠ 6, ∠ 3 and ∠ 7, ∠ 4 and ∠ 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.
