Line and Angle Relationships Sec 6'1

1
Line and Angle RelationshipsSec 6.1

• GOALS
• To learn vocabulary
• To identify angles and relationships of angles
  formed by tow parallel lines cut by a transversal

2
Vocabulary
Line
l
B
A
Ray
A
B
Angle
A
sides
vertex
B
C
3
Types of Angles

• Acute angles angles that have measures between
  0 and
• Right angles angles that have measures equal to
  
• Obtuse angles angles that have measures between
• Straight angles angles that have measures equal
  to

4
Special Pairs of Angles

• Vertical angles opposite angles formed by
  intersecting lines. Vertical angles are
  congruent.

5
Special Pairs of Angles

• Adjacent angles angles that have the same
  vertex, share a common side, and do not overlap.

A
B
C
6
Special Pairs of Angles

• Complementary angles angles whose sum is

A
D
B
C
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Special Pairs of Angles

• Supplementary angles angles whose sum is

A
B
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Examples
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Perpendicular Lines

• Perpendicular lines lines that intersect at
  right angles

h
k
10
Parallel Lines

• Parallel lines two lines in a plane that never
  intersect or cross

h
k
11
Transversal

• A line that intersects two or more other lines
  is called a transversal. Eight angles are formed
  when a transversal intersect two lines.
• 
  
  

t
2
1
4
3
6
5
7
8
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Corresponding Angles Postulate

• Corresponding angles are those in the same
  position on the two lines in relation to the
  transversal.
• If two parallel lines are cut by a transversal,
  then corresponding angles are congruent.
• 
  
  

2
1
4
3
6
5
7
8
13
Alternate Interior Angles Theorem

• Alternate interior angles are those on opposite
  sides of the transversal and inside the other two
  lines.
• If two parallel lines are cut by a transversal,
  then alternate interior angles are congruent.
• 
  
  

2
1
4
3
6
5
7
8
14
Alternate Exterior Angles Theorem

• Alternate exterior angles are those on opposite
  sides of the transversal and outside the other
  two lines.
• If two parallel lines are cut by a transversal,
  then alternate exterior angles are congruent.

2
1
4
3
6
5
7
8
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Example

• Given
• Find x
• 
  
  

h
k
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Example

• Given
• Find x and the angle measure
• 
  
  
• 
  
  

k
h
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Example

• Given
• Find the angles shown.
• 
  
  

118
2
k
3
5
4
h
18
Students

• Given
• Find All other angle measures
• 
  
  

h
k
19
Homework

• Page 259 13-15, 19-22, 30-33, 47-49