Now we are asked to describe two ways in which we can show that ∠ 1 is congruent to ∠ 7. Before we do that, let's review the definitions of different types of angle pairs.
They lie outside the two lines on opposite sides of the transversal.
We can see that ∠ 1 and ∠ 7 lie on opposite sides on the transversal outside of the parallel lines, so these angles are alternate exterior angles.
When a transversal intersects parallel lines, alternate exterior angles are congruent. Because of that, ∠ 1 and ∠ 7 are congruent.
∠ 1 and ∠ 7 are congruent because they are alternate exterior angles.
Let's think of another way of showing that these angles are congruent. First, we can see that ∠ 1 and ∠ 5 are corresponding angles because they lie in corresponding positions on the same side of the transversal.
When a transversal intersects parallel lines, corresponding angles are congruent. This means that ∠ 1=∠ 5. Next, notice that ∠ 5 and ∠ 7 lie on the opposite sides of the point of intersection of two lines, meaning that these angles are vertical.
Because vertical angles are congruent, we know that ∠ 5 and ∠ 7 are congruent. Therefore, ∠ 1 is congruent to ∠ 7.
∠ 1 and ∠ 7 are congruent because ∠ 1 and ∠ 5 are corresponding angles and ∠ 5 and ∠ 7 are vertical angles.
Notice that these are only two example ways of showing that ∠ 1 and ∠ 7 are congruent and there are more possible solutions.
