The document examines corresponding angles ∠1 and ∠5 that are shown not to be congruent in a diagram. It describes tilting line m until the angles become congruent, at which point the lines can be seen to be parallel. It then states the theorem that if two lines are cut by a transversal such that the corresponding angles are congruent, then the lines are parallel. This is the converse of the postulate that parallel lines cut by a transversal form congruent corresponding angles.

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m
n
t
Let’s look at a pair of corresponding angles, ∠1 and ∠5.
We can see in the figure, that ∠1 and ∠5 are not congruent
(by inspection) and that the lines are not parallel.
Let’s imagine that we tilt line m until ∠1 ≅ ∠5

2. 1
2
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m
n
t
Let’s look at a pair of corresponding angles, ∠1 and ∠5.
We can see in the figure, that ∠1 and ∠5 are not congruent
(by inspection) and that the lines are not parallel.
Let’s imagine that we tilt line m until ∠1 ≅ ∠5

3. 1
2
3
4
5
6
7
8
m
n
t
Let’s look at a pair of corresponding angles, ∠1 and ∠5.
We can see in the figure, that ∠1 and ∠5 are not congruent
(by inspection) and that the lines are not parallel.
Let’s imagine that we tilt line m until ∠1 ≅ ∠5

4. 1
2
3
4
5
6
7
8
m
n
t
Let’s look at a pair of corresponding angles, ∠1 and ∠5.
We can see in the figure, that ∠1 and ∠5 are not congruent
(by inspection) and that the lines are not parallel.
Let’s imagine that we tilt line m until ∠1 ≅ ∠5

5. 1
2
3
4
5
6
7
8
m
n
t
Let’s look at a pair of corresponding angles, ∠1 and ∠5.
We can see in the figure, that ∠1 and ∠5 are not congruent
(by inspection) and that the lines are not parallel.
Let’s imagine that we tilt line m until ∠1 ≅ ∠5

6. 1
2
3
4
5
6
7
8
m
n
t
Let’s look at a pair of corresponding angles, ∠1 and ∠5.
We can see in the figure, that ∠1 and ∠5 are not congruent
(by inspection) and that the lines are not parallel.
Let’s imagine that we tilt line m until ∠1 ≅ ∠5

7. 1
2
3
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5
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8
m
n
tNow that ∠1 ≅ ∠5, 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, ∠1 and ∠5.
We can see in the figure, that ∠1 and ∠5 are not congruent
(by inspection) and that the lines are not parallel.
Let’s imagine that we tilt line m until ∠1 ≅ ∠5

8. 1
2
3
4
5
6
7
8
m
n
tNow that ∠1 ≅ ∠5, 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, ∠1 and ∠5.
We can see in the figure, that ∠1 and ∠5 are not congruent
(by inspection) and that the lines are not parallel.
Let’s imagine that we tilt line m until ∠1 ≅ ∠5

9. 1
2
3
4
5
6
7
8
m
n
tNow that ∠1 ≅ ∠5, 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, ∠1 and ∠5.
We can see in the figure, that ∠1 and ∠5 are not congruent
(by inspection) and that the lines are not parallel.
Let’s imagine that we tilt line m until ∠1 ≅ ∠5