1.5 Angle Pairs .notebook
August 30, 2016
8/30/16 - Warm Up Problem
Find the value of x and the lengths
of LM and MN if LN = 28
3x
L
5x - 4
M
N
Sep 4­12:11 PM
1
1.5 Angle Pairs .notebook
August 30, 2016
Section 1.5 - Angle Pairs
Goal: Identify and find measures of special pairs of angles
When lines intersect,
several angles are formed.
The measures of these
angles have special
relationships.
2
3
4
1
60o
· Certain pairs of angles have special names and special relationships
Sep 6­5:58 PM
2
1.5 Angle Pairs .notebook
August 30, 2016
Special Pairs of Angles
Angle Pair
Description
Example
Adjacent Angles
· share one side
· share a vertex
· have no common interior points
Vertical Angles
· are nonadjacent
· sides are opposite rays
· are always congruent
· measures add to 90o
·
Complementary can be adjacent or nonadjacent
Angles
· each angle is called the complement of the other
· measures add to 180o
· can be adjacent or Supplementary nonadjacent
Angles
· each angle is called the supplement of the other
Linear Pair: a pair of adjacent angles whose non­
common sides are opposite rays
Postulate 1-9: Linear Pair Postulate
If two angles for a linear pair, then they are
________________.
Sep 6­6:01 PM
3
1.5 Angle Pairs .notebook
August 30, 2016
Identify each special pair of angles.
Adjacent, Vertical, Supplementary, or Complementary
1
3
2
4
10
9
7
5 6
11 12
8
Sep 6­6:07 PM
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1.5 Angle Pairs .notebook
August 30, 2016
Identifying Angle Pairs
Is each statement true? Explain.
<BFD and <CFD are adjacent angles.
B
28o
A
<AFB and <EFD are vertical angles.
62o
F
118o
C
D
E
<AFE and <BFC are complementary angles.
Aug 30­3:05 PM
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1.5 Angle Pairs .notebook
August 30, 2016
Interpreting Diagrams
If a diagram has no marks or measures
included on it, some information can be
concluded from the diagram and some
cannot.
D
A
E
B
C
Finding Information from a Diagram
There are some relationships you can conclude such as:
- Angles are adjacent
- Angles are adjacent and supplementary (linear pair)
- Angles are vertical angles
There are some relationships you CANNOT conclude:
- Angles or segments are congruent
- An angle is a right angle
- Angles are complementary
Sep 3­3:45 PM
6
1.5 Angle Pairs .notebook
August 30, 2016
Can you conclude each statement from the diagram?
Explain.
2
1
and
3
5
4
are complementary
Sep 3­3:51 PM
7
1.5 Angle Pairs .notebook
Assignment:
pg. 38
(7-23)
August 30, 2016
Make sure you EXPLAIN your
answers!
Aug 30­3:11 PM
8