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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
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