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Lesson 11.1 Angle and Line Relationships.
Vertical Angles - Opposite angles that are formed by intersecting lines.
Opposite angles (vertical angles) are ALWAYS congruent.
b
a
ba
Adjacent Angles
• Share a vertex and a side but no points in the interiors.
A
X
B
C
<AXB and <BXC are adjacent
angles
<AXC and <BXC are not adjacent angles
Why?
Complementary Angles
ab
- Angles whosesum is 90 .
m a m b 90
x y
m x m y 90
Complementary angles do nothave to be adjacent.
Supplementary Angles
kt
- Angles whosesum is 180 .
m k m t 180
b c
m b m c 180
Supplementary angles do nothave to be adjacent.
(4n 30)
Find the value of n.
(n 10) (2n 30)
n
1) 2)
n (2n 30) 90 3n 30 90
30 30 3n 603 3n 20
(4n 30) (n 10) 180 5n 20 180
20 20 5n 1605 5n 32
Congruent Angles
• Angles that have the same measurement• Notation:
1 3
1 3m m
Lines
Identifying Corresponding Angles Transversal -A line that intersects
two other lines.
Identifying Corresponding Angles CorrespondingAngles
- Two angles that are formed by two lines and a transversal and occupy corresponding positions.
A B
C D
1 23 4
5 67 8
If the two lines are parallel, then the corresponding angles are congruent.
Corresponding Angles1 52 63 74 8
Identifying Alternate Interior Angles Alternate Interior Angles:-interior of a pair of lines on opposite
sides of the transversal.A B
C D
1 23 4
5 67 8
If the two lines are parallel, then the alternate interior angles are congruent.
Corresponding Angles3 64 5
Identifying Alternate Exterior Angles Alternate Exterior Angles:-on opposite sides of the transversal
and outside the parallel linesA B
C D
1 23 4
5 67 8
If the two lines are parallel, then the alternate exterior angles are congruent.
Corresponding Angles1 82 7
Homework
11.1 worksheet