Download 1.6 Angle Pair Relationships

1.6 Angle Pair
Relationships
Geometry
Ms. Reser
Fall 2005
Standards/Objectives
:
Standard 3: Students will understand
geometric concepts and applications.
Objectives:
• Identify vertical angles and linear pairs.
• Identify complementary and
supplementary angles.
Assignment:
• pp. 47-49 #4-36 all; 41-51 odd
Which angles are adjacent?
1 &  2,  2 &  3,  3 &  4,
 4&  1
Then what do we call  1 &
 3?
2
1
3
4
Vertical Angles – 2 angles
that share a common vertex &
whose sides form 2 pairs of
opposite rays.
 1 &  3,  2 &  4
Linear Pair (of
angles)
• 2 adjacent angles whose noncommon sides are opposite rays.
Example
• Vertical angles?
1 & 4
• Adjacent angles?
2
1 & 2, 2 & 3,
1
3
3 & 4, 4 & 5, 5 & 1 5 4
• Linear pair?
5 & 4, 1 & 5
• Adjacent angles not a linear pair?
1 & 2, 2 & 3, 3 & 4
Important Facts
• Vertical Angles are congruent.
• The sum of the measures of the angles in
a linear pair is 180o.
Example:
• If m 5=130o, find
m 3 = 130°
m 6 = 50°
m 4 = 50°
4
5
3
6
A
Example:
E
B
• Find x
y
m ABE
m ABD
m DBC
m EBC
D
C
x=40
y=35
m ABE=125o
m ABD=55o
m  DBC=125o
m  EBC=55o
Complementary Angles
• 2 angles whose sum is 90o
35o
1
2
1 & 2 are complementary
A & B are complementary
55o
A
B
Supplementary
Angles
• 2 angles whose sum is 180o
1 & 2 are
supplementary.
X & Y are
supplementary.
130o
X
50o
Y
Ex: A & B are
supplementary. mA is 5
times mB. Find mA &
mB.
mA + mB = 180o
mA = 5(mB)
Now substitute!
5(mB) + mB = 180o
6(mB)=180o
mB=30o
mA=150o