# Unit 6 Parallel Lines - PowerPoint PPT Presentation

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## Unit 6 Parallel Lines

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### Unit 6 Parallel Lines Learn about parallel line relationships Prove lines parallel Describe angle relationship in polygons – PowerPoint PPT presentation

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Title: 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