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Lesson Parallel Lines and Transversals
There are several types of angle pairs
in parallel lines
cut by a transversal
The word 'alternate' means
on opposite sides of the transversal

Angles that are alternate to ∡1
7
5
8
3
6
1
4
2
would be
on opposite sides
because they are
∡2
∡4
∡6
∡8
∡1 is on this side
The word 'alternate' means
on opposite sides of the transversal
Angles that are alternate to ∡1
7
5
8
3
6
1
4
2
would be
on opposite sides
because they are
∡2
∡4
∡6
∡8
∡1 is on this side
The word 'alternate' means
on opposite sides of the transversal
Angles that are alternate to ∡1
7
5
the rest are on this side
8
3
6
1
4
2
would be
on opposite sides
because they are
∡2
∡4
∡6
∡8
Which angle is alternate to ∡5
∡1
∡3
∡4
7
5
8
3
6
1
4
2
Which angle is alternate to ∡8
∡1
∡2
∡4
7
5
8
3
6
1
4
2
Which angles are alternate to ∡6
∡1
∡2
∡3
7
5
8
3
6
1
4
2
∡4
∡5
∡7
∡8
The phrase 'same side' means
on the same side of the transversal
1
4
2
5
3
7
6
8
The phrase 'same side' means
The angles on the same side as ∡1 are
on the same side of the transversal
1
4
2
5
3
7
6
8
The phrase 'same side' means
The angles on the same side as ∡1 are
on the same side of the transversal
1
4
2
5
3
7
6
because they are on the 
8
∡4
∡5
∡7
The phrase 'same side' means
The angles on the same side as ∡1 are
on the same side of the transversal
1
4
2
5
3
7
6
because they are on the 
8
same side as ∡1
∡4
∡5
∡7
∡1 is on this side
The phrase 'same side' means
The angles on the same side as ∡1 are
on the same side of the transversal
1
4
2
5
3
7
6
because they are on the 
8
same side as ∡1
∡4
∡5
∡7
and so are the others
∡1 is on this side
The phrase 'same side' means
The angles on the same side as ∡1 are
on the same side of the transversal
1
4
2
5
3
7
6
because they are on the 
8
same side as ∡1
∡4
∡5
∡7
Which angle is same side to ∡5
∡1
∡2
∡4
7
5
8
3
6
1
4
2
Which angle is same side to ∡8
∡1
∡3
∡4
7
5
8
3
6
1
4
2
Which angles are same side to ∡6
∡1
∡2
∡3
7
5
8
3
6
1
4
2
∡4
∡5
∡7
∡8
The word 'interior' means
in between the parallel lines
The interior angles are
1
4
2
5
3
7
6
8
∡4
∡3
∡5
∡6
because they are
between the parallel
lines
The word 'interior' means
in between the parallel lines
The interior angles are
1
4
2
5
3
7
6
8
∡4
∡3
∡5
∡6
because they are
between the parallel
lines
Which angle is an interior angle
∡1
∡3
∡8
7
5
8
3
6
1
4
2
Which angles are interior
∡1
∡2
∡3
∡6
∡5
∡4
7
5
8
∡8
∡7
3
6
1
4
2
The word 'exterior' means
angles outside the parallel lines
The exterior angles would be
1
4
2
5
3
7
6
8
because they are outside
the parallel lines
∡1
∡2
∡7
∡8
Which angle is an exterior angle
∡6
∡3
∡8
7
5
8
3
6
1
4
2
Which angles are exterior
∡1
∡2
∡3
∡6
∡5
∡4
7
5
8
∡8
∡7
3
6
1
4
2
Interior
Same Side
Exterior
Alternate
Outside
?
In between
?
Same Side
?
Opposite
?
∡8 is
interior
exterior
7
5
8
6
3
1
4
2
∡2 is
interior
exterior
7
5
8
6
3
1
4
2
∡8 and 3 are
7
5
Alternate
Same Side
8
6
3
1
4
2
Now that you learned the vocabulary,
it's time to learn the names of the angles thatwould be used in proofs. 
would be both
An alternate interior angle
1
4
2
opposite sides of the transversal
5
3
7
6
inside the parallel lines
The alternate interior to ∡3
8
and
would be angle 5.
Alternate Interior to ∡6
7
5
8
6
3
1
4
∡1
∡2
∡3
2
∡4
∡5
∡7
∡8
The same side interior angle to ∡5
would be on the same side of the transversal
and in between the parallel lines
1
4
2
5
7
3
6
8
Same side interior to ∡6
7
5
8
6
3
1
4
∡1
∡2
∡3
2
∡4
∡5
∡7
∡8
There are four angles around each intersection
Top Left
Bottom Left
Corresponding angles 
have to do with position
Top Right
Bottom Right
Top Left
Bottom Left
Bottom Left
Top Left
Top Right
Bottom Right
Top Right
Bottom Right
Bottom Left
Top Left
Bottom Left
?
Top Left
?
Top Right
Bottom Right
Top Right
?
Bottom Right
?
Each angle that has the same name is a
Top Left
Bottom Left
Bottom Left
Top Left
corresponding angle
Top Right
Bottom Right
Top Right
Bottom Right
Which angle corresponds to ∡5
1
3
2
5
4
7
6
8
∡1
∡2
∡3
∡4
∡6
∡7
∡8
These are also known as consecutive interior angles.


angles add upto 180 degrees. 
Same side interior
60
120
120
60
60
120
120
60
These are also known as consecutive interior angles.

Same side interior
60
120
120
60
60
120
120
60

angles add upto 180 degrees. 
Same side exterior
60
120
120
60
60
120
120
60
angles also add up
to 180 degrees. 
60
120
120
60
60
120
120
60
The same side exterior angles also add upto 180 degrees. 
angles are congruent.

That means they have the same angle measurement.
 Alternate exterior angles 
60
120
120
60
60
120
120
60
 This is another pair of alternate exterior angles. 
60
120
120
60
60
120
120
60
angles are congruent

That means they have the same angle measurement.
Alternate interior angles
60
120
120
60
60
120
120
60
 This is another pair of alternate interior angles 
60
120
120
60
60
120
120
60
vertical angles are congruent
 (have the same measurement).
60
 Vertical angles
120
120
60
60
120
120
60
vertical angles are congruent
 (have the same measurement).
60
120
120
60
60
120
120
60
vertical angles are congruent
 (have the same measurement).
60
120
120
60
60
120
120
60
vertical angles are congruent
 (have the same measurement).
60
120
120
60
60
120
120
60
Supplementary angles that add up to 180°.
 Linear pairs
60
120
120
60
60
120
120
60
60
120
120
60
60
120
120
60
60
120
120
60
60
120
120
60
60
120
120
60
60
120
120
60
60
120
120
60
60
120
120
60
60
120
120
60
60
120
120
60
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Parallel Lines and Transversal
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