1

2

3

4

5

6

78

mn

t

Let’s look at a pair of corresponding angles, .

We can see in the figure, that and are not congruent (by inspection) and that the lines are not parallel.

Let’s imagine that we tilt line m until

1

2

3

4

5

6

78

mn

t

Let’s look at a pair of corresponding angles, .

We can see in the figure, that and are not congruent (by inspection) and that the lines are not parallel.

Let’s imagine that we tilt line m until

1

2

3

4

5

6

78

mn

t

Let’s look at a pair of corresponding angles, .

We can see in the figure, that and are not congruent (by inspection) and that the lines are not parallel.

Let’s imagine that we tilt line m until

1

2

3

4

5

6

78

mn

t

Let’s look at a pair of corresponding angles, .

We can see in the figure, that and are not congruent (by inspection) and that the lines are not parallel.

Let’s imagine that we tilt line m until

1

2

3

4

5

6

78

mn

t

Let’s look at a pair of corresponding angles, .

We can see in the figure, that and are not congruent (by inspection) and that the lines are not parallel.

Let’s imagine that we tilt line m until

1

2

3

4

5

6

78

mn

t

Let’s look at a pair of corresponding angles, .

We can see in the figure, that and are not congruent (by inspection) and that the lines are not parallel.

Let’s imagine that we tilt line m until

1

2

3

4

5

6

78

mn

tNow that , we can see that the lines are parallel as a result. This result can be proved, but only by a method called indirect proof which we do not cover. Therefore, we will just assume that the following is true:

Let’s look at a pair of corresponding angles, .

We can see in the figure, that and are not congruent (by inspection) and that the lines are not parallel.

Let’s imagine that we tilt line m until

1

2

3

4

5

6

78

mn

tNow that , we can see that the lines are parallel as a result. This result can be proved, but only by a method called indirect proof which we do not cover. Therefore, we will just assume that the following is true:

Theorem: If two lines are cut by a transversal so that the corresponding angles are congruent, then these lines are parallel.

Let’s look at a pair of corresponding angles, .

We can see in the figure, that and are not congruent (by inspection) and that the lines are not parallel.

Let’s imagine that we tilt line m until

1

2

3

4

5

6

78

mn

tNow that , we can see that the lines are parallel as a result. This result can be proved, but only by a method called indirect proof which we do not cover. Therefore, we will just assume that the following is true:

Theorem: If two lines are cut by a transversal so that the corresponding angles are congruent, then these lines are parallel.

This theorem is the converse of the postulate from the previous section that states:

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

Let’s look at a pair of corresponding angles, .

We can see in the figure, that and are not congruent (by inspection) and that the lines are not parallel.

Let’s imagine that we tilt line m until