Discovering Angle Relationships

1
Discovering Angle Relationships

• Objectives
• Discover relationships between special pairs
  of angles.

2
complimentary angles - two angles that add to
90
3
30
60

• This pair is complimentary because 60 30 90.

4
Yes. 454590
45
45

• Is this pair of angles complimentary?

5
No. They must be a pair of angles that add to 90.
30
30
30

• Are these angles complimentary?

6
supplimentary angles - two angles that add to
180
7
120
60

• This pair is supplimentary because 60 120 180.

8
No. 9782179.
97
82

• Are these angles supplimentary?

9
Yes. 47133180.
47
133

• Are these angles supplimentary?

10
vertical angles - two angles that share a
vertex and are directly across from each
other created by two crossing lines
11
B
?BEA ?DEC
D
A
E
C

• ?AEB ?CED are vertical angles. Name the other
  pair of vertical angles here.

12
Yes. They share a vertex and are across from one
another.
I
F
H
K
G

• Are ?FHI ?GHK vertical angles?

13
No. They are supplimentary.
I
F
H
K
G

• Are ?FHI ?IHK vertical angles?

14
linear pair of angles - two angles that share
a vertex form a straight line (add to 180)
15
B
D
130
A
50
E

• ?AEB ?BED are a linear pair of angles. They
  form a straight line 50130180.

16
No. They are vertical angles.
I
F
H
G
K

• Are ?FHI ?GHK a linear pair of angles?

17
Yes - they form a straight line.
I
F
H
G
K

• Are ?FHI ?GHF a linear pair of angles?

18
No. They do not share a vertex. They are
supplimentary though.
D
C
O
30
G
150
A
T

• Are ?CAT ?DOG a linear pair of angles?

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Compare the measures of vertical angles here...

• C-15 Vertical Angles Conjecture - If two angles
  are vertical angles, then they are congruent.

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• C-16 Linear Pair Conjecture - If two angles are
  a linear pair, then their sum is 180.

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A
B
C
75
m?A?
75
105
m?B?
105
m?C?
22
A
57
B
C
33
m?A?
33
90
m?B?
57
m?C?