Parallel Lines with Transversals

1. Parallel Lines and
Transversals

2. A
B
D
C
Parallel Lines and Transversals
What would you call two lines which do not intersect?
Parallel
A solid arrow placed
on two lines of a
diagram indicate the
lines are parallel.
The symbol || is used to
indicate parallel lines.
AB || CD

3. Parallel Lines and Transversals
A slash through the parallel symbol || indicates the
lines are not parallel.
AB || CD
A
D
B
C

4. Parallel Lines and Transversals
Transversal -
A transversal is a line which intersects two or more
lines in a plane. The intersected lines do not have to
be parallel.
t
mkj
Lines j, k, and m
are intersected
by line t.
Therefore, line t
is a transversal
of lines j, k, and
m.

5. Parallel Lines and Transversals
Identifying Angles -
t
k
j
1
2
3
4
5
6
7
8
Exterior angles are
on the exterior of
the two lines cut by
the transversal.
The exterior angles are:
<1, <7, <2, <8

6. Parallel Lines and Transversals
Identifying Angles -
t
k
j
1
2
3
4
5
6
7
8
Interior angles
are on the
interior of the
two lines cut by
the transversal.
The interior angles are:
<3, <5, <4, <6

7. Parallel Lines and Transversals
Identifying Angles -
t
kj
1
2
3
4
5
6
7
8
Alternate interior
angles are on the
interior of the two
lines and on opposite
sides of the
transversal.
Alternate interior angles are:
<3 & <6, <4 & <5

8. Parallel Lines and Transversals
Identifying Angles -
t
k
j
1
2
3
4
5
6
7
8
Alternate
exterior angles
are on the
exterior of the
two lines and on
opposite sides
of the
transversal.
Alternate exterior angles are:
<1 & <8, <2 & <7

9. Parallel Lines and Transversals
Identifying Angles -
t
k
j
1
2
3
4
5
6
7
8
Corresponding
angles are on the
corresponding
side of the two
lines and on the
same side of the
transversal.
Corresponding angles are:
<1 & <5, <3 & <7, <2 & <6, <4 & <8

10. 2. < 2 and < 10 are
alternate interior angles.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
1
2
3
4
5
6
78
9
101112
13141516
Determine if the statement is true or false. If false,
correct the statement.
1.Line r is a transversal
of lines p and q.

11. 2. < 2 and < 10 are
alternate interior angles.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
1
2
3
4
5
6
78
9
101112
13141516
Determine if the statement is true or false. If false,
correct the statement.
1.Line r is a transversal
of lines p and q.
True – Line r intersects
both lines in a plane.
False - The angles are
corresponding angles on
transversal p.

12. 4. < 1 and < 15 are
alternate exterior angles.
1.<3 and < 5 are alternate
interior angles.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
1
2
3
4
5
6
78
9
101112
13141516
Determine if the statement is true or false. If false,
correct the statement.

13. 4. < 1 and < 15 are
alternate exterior angles.
3. < 3 and < 5 are
alternate interior angles.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
1
2
3
4
5
6
78
9
101112
13141516
Determine if the statement is true or false. If false,
correct the statement.
False – The angles are
vertical angles created
by the intersection of q
and r.
True - The angles are
alternate exterior angles
on transversal p.

14. 6. < 10 and < 11 are
consecutive interior angles.
5. < 6 and < 12 are
alternate interior angles.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
1
2
3
4
5
6
78
9
101112
13141516
Determine if the statement is true or false. If false,
correct the statement.

15. 6. < 10 and < 11 are
consecutive interior angles.
5. < 6 and < 12 are
alternate interior angles.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
1
2
3
4
5
6
78
9
101112
13141516
Determine if the statement is true or false. If false,
correct the statement.
True – The angles are
alternate interior angles
on transversal q.
True – The angles are
consecutive interior
angles on transversal s.

16. Determine if the statement is true or false. If false,
correct the statement.7. < 3 and < 4 are alternate
exterior angles.
8. < 16 and < 14 are
corresponding angles.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
1
2
3
4
5
6
78
9
101112
13141516

17. Determine if the statement is true or false. If false,
correct the statement.7. < 3 and < 4 are alternate
exterior angles.
8. < 16 and < 14 are
corresponding angles.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
1
2
3
4
5
6
78
9
101112
13141516
False– The angles are
adjacent angles on
transversal r.
True – The angles are
corresponding angles
on transversal s.