Unit 6 Parallel Lines

1
Unit 6Parallel Lines

• Learn about parallel line relationships
• Prove lines parallel
• Describe angle relationship in polygons

2
Lecture 1

• Objectives
• State the definition of parallel lines
• Describe a transverse

3
Parallel Lines

• Coplanar lines that do not intersect.

m
m n
n
Skew lines are non-coplanar, non-intersecting
lines.
4
The Transversal

• Any line that intersects two or more coplanar
  lines.

5
Special Angle Pairs
t

• Corresponding
• ?1 and ? 5
• Alternate Interior
• ? 4 and ? 5
• Same Side Interior
• ? 4 and ? 6

1
2
3
4
r
5
6
s
7
8
6
Lecture 2

• Objectives
• Learn the special angle relationships
• 
  when lines
• 
  are parallel

7
When parallel lines are cut by a transversal

• Corresponding ?s ?
• ?1 ? ? 5
• Alternate Interior ?s ?
• ? 4 ? ? 5
• Same Side Interior ?s Suppl.
• ? 4 suppl. ? 6

8

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

9

• If two parallel lines are cut by a
  transversal, then alternate interior angles are
  congruent.

10

• If two parallel lines are cut by a
  transversal, then same side interior angles are
  supplementary.

11

• A line perpendicular to one of two parallel
  lines is perpendicular to the other.

t
r
s
12
Lecture 3

• Objectives
• Learn about ways to prove lines are parallel

13

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

If ?1? ? 2, then m n.
1
m
2
n
14

• If two lines are cut by a transversal so that
  alternate interior angles are congruent, then the
  lines are parallel.

If ?1? ? 2, then m n.
m
1
2
n
15

• If two lines are cut by a transversal so that
  same side interior angles are supplementary, then
  the lines are parallel.

If ?1 suppl ? 2, then m n.
m
1
2
n
16

• In a plane, two lines perpendicular to the same
  line are parallel.

If t ? m and t ? n , then m n.
t
m
n
17

• Two lines parallel to the same line are parallel
  to each other

If p ?? m and m ?? n, then p ?? n
p
m
n
18
Ways to Prove Lines are Parallel

• Corresponding angles are congruent
• Alternate interior angles are congruent
• Same side interior angles are supplementary
• In a plane, that two lines are perpendicular to
  the same line
• Both lines are parallel to a third line