Download Complementary Angles

Lesson 9.2
Angle Relationships and Parallel
Lines
.
Types of Angles
Acute - Angles
that measure
less than 90.
Right - Angles
that measure
exactly 90.
Obtuse -Angles that
measure more than 90
and less than 180.
Adjacent Angles
• Share a vertex and a side but no points in the
interiors.
<AXB and <BXC
are adjacent
angles
B
A
X
C
<AXC and <BXC are not
adjacent angles
Why?
Complementary Angles - Angles whose
sum is 90 .
a
b
ma  mb  90
x
y
mx  my  90
Complementary
angles do not
have to be
adjacent.
Supplementary Angles - Angles whose
sum is 180 .
k
t
mk  mt  180
b
c
mb  mc  180
Supplementary
angles do not
have to be
adjacent.
Congruent Angles
• Angles that have the same measurement
• Notation:
 1  3
m 1 m  3
Vertical Angles - Opposite angles that are
formed by intersecting lines.
a
Opposite angles (vertical angles)
are ALWAYS congruent.
b
a  b
Identifying Corresponding Angles
Transversal -A line that intersects
two other lines.
Identifying Corresponding Angles
Corresponding - Two angles that are formed by two
lines and a transversal and occupy
Angles
corresponding positions.
A
C
1 2
3 4
5 6
7 8
B
D
Corresponding Angles
If the two lines are parallel,
then the corresponding
angles are congruent.
1  5
2  6
3  7
4  8
Identifying Alternate Interior Angles
Alternate Interior Angles:
-interior of a pair of lines on opposite sides of
the transversal.
A
C
1 2
3 4
5 6
7 8
B
D
Corresponding Angles
If the two lines are parallel,
then the alternate interior
angles are congruent.
3  6
4  5
Find the value of n.
1)
2)
n
(4n  30)
(n  10)
(2n  30)
n  (2n  30)  90
3n  30  90
30  30
3n  60
3 3
n  20
(4n  30)  (n  10)  180
5n  20  180
20  20
5n  160
5 5
n  32
Homework
• Page 452 -453 (1-11 all and 13)
• Draw figures in the homework