4. 1
2
3
4
5
6
7
8
m n
t
Interior angles are angles that are between the lines.
∠3, ∠4, ∠5, and ∠6 are interior angles.
Exterior angles are angles that are outside the lines.
5. 1
2
3
4
5
6
7
8
m n
t
Interior angles are angles that are between the lines.
∠3, ∠4, ∠5, and ∠6 are interior angles.
Exterior angles are angles that are outside the lines.
∠1, ∠2, ∠7, and ∠8 are exterior angles.
7. 1
2
3
4
5
6
7
8
m n
t
Corresponding angles are angles that are in the same relative
positions when compared to the points of intersection.
∠1 and ∠5 are a pair of corresponding angles because they are
both up and to the left of the points of intersection.
8. 1
2
3
4
5
6
7
8
m n
t
Corresponding angles are angles that are in the same relative
positions when compared to the points of intersection.
∠1 and ∠5 are a pair of corresponding angles because they are
both up and to the left of the points of intersection.
9. 1
2
3
4
5
6
7
8
m n
t
Corresponding angles are angles that are in the same relative
positions when compared to the points of intersection.
∠1 and ∠5 are a pair of corresponding angles because they are
both up and to the left of the points of intersection.
∠3 and ∠7 are a pair of corresponding angles because they are
both up and to the right of the points of intersection.
10. 1
2
3
4
5
6
7
8
m n
t
Corresponding angles are angles that are in the same relative
positions when compared to the points of intersection.
∠1 and ∠5 are a pair of corresponding angles because they are
both up and to the left of the points of intersection.
∠3 and ∠7 are a pair of corresponding angles because they are
both up and to the right of the points of intersection.
∠2 and ∠6 are a pair of corresponding angles because they are
both down and to the left of the points of intersection.
11. 1
2
3
4
5
6
7
8
m n
t
Corresponding angles are angles that are in the same relative
positions when compared to the points of intersection.
∠1 and ∠5 are a pair of corresponding angles because they are
both up and to the left of the points of intersection.
∠3 and ∠7 are a pair of corresponding angles because they are
both up and to the right of the points of intersection.
∠2 and ∠6 are a pair of corresponding angles because they are
both down and to the left of the points of intersection.
∠4 and ∠8 are a pair of corresponding angles because they are
both down and to the right of the points of intersection.
14. 1
2
3
4
5
6
7
8
m n
t
Alternate interior angles are interior angles that are on opposite
sides of the transversal.
∠3 and ∠6 are alternate interior angles.
∠4 and ∠5 are another pair of alternate interior angles.
17. 1
2
3
4
5
6
7
8
m n
t
Alternate exterior angles are exterior angles that are on
opposite sides of the transversal.
∠1 and ∠8 are alternate exterior angles.
∠2 and ∠7 are another pair of alternate exterior angles.
18. m
n
Parallel lines are lines that will never intersect, no matter how
far we extend them.
We can write m||n.
20. 1
2
3
4
5
6
7
8
m
n
t
When m and n are parallel, we get many nice relationships
between the pairs of angles.
Postulate: If two parallel lines are cut by a transversal, then
the corresponding angles are congruent.
So if m||n, then ∠1 and ∠5 are congruent.
21. 1
2
3
4
5
6
7
8
m
n
t
When m and n are parallel, we get many nice relationships
between the pairs of angles.
Theorem: If two parallel lines are cut by a transversal, then
the alternate interior angles are congruent.
So if m||n, then ∠3 and ∠6 are congruent.
22. 1
2
3
4
5
6
7
8
m
n
t
When m and n are parallel, we get many nice relationships
between the pairs of angles.
Theorem: If two parallel lines are cut by a transversal, then
the alternate exterior angles are congruent.
So if m||n, then ∠1 and ∠8 are congruent.
23. 1
2
3
4
5
6
7
8
m
n
t
When m and n are parallel, we get many nice relationships
between the pairs of angles.
Theorem: If two parallel lines are cut by a transversal, then
the interior angles on the same side of the transversal are
supplementary.
So if m||n, then ∠3 and ∠5 are supplementary.
24. 1
2
3
4
5
6
7
8
m
n
t
When m and n are parallel, we get many nice relationships
between the pairs of angles.
Theorem: If two parallel lines are cut by a transversal, then
the exterior angles on the same side of the transversal are
supplementary.
So if m||n, then ∠2 and ∠8 are supplementary.
25. 1
2
3
4
5
6
7
8
m n
t
It is very important to remember that these relationships are
only true when the lines are parallel.
In the figure, we see that m and n are not parallel and ∠1 and
∠5 are obviously not congruent.