Name _______________________________________
Date ____________________
Hour ______
Notes: Section 1.6 - Exploring Angles
Modern Geometry A
Definition: A _______ is a part of a line that goes on forever in ________________. It has one ___________.
We name rays with its endpoint first and __________________________________ second.
Example: This is ray AB or AB

Example: This is ray PU or PU

A
B
U
P
Definition: Opposite Rays are rays that leave _____________________ in ________________________.
They make a _________.
Example: OD and OG are opposite rays 
D
O
G
Definition: When two rays (or segments) leave from the same endpoint, an ________ is formed.
* Parts of angles you need to know:
Exter ior
Side
Inter ior
Vertex
Side
Exter ior
Exter ior
We name an angle three ways:
1) Use three points – a point from each side, and the _________. The _________ must be in the ___________.
2) A number in the ____________ of the angle, near the vertex.
3) If there’s only one angle in the drawing, you can use the vertex only.
Example: This angle can be named:
P
1)  PIG or  GIP
2)  3
3)  I
3
I
G
Example: Name all the angles in this picture:
M
K
3
4
A
R
We measure angles in __________. This is not a length, but how far “open” the angle is.
Example: The measure of  A  48 or m  A  48 .
OR…
B
48
A
D
* Angle Addition Postulate:
m  SNW  m  WDO  m  SNO
S
W
N
O
Example:
If m  JAE  20 and m  JAN  60 , find m  NAE .
J
Example:
E
If m  JAE  2x  20 , m  EAN  x  10 and
m  JAN  57 , find x and m  JAE .
A
N
Section 1.6 (continued)
There are four types of angles we’ll be working with:

1) Acute - Measures less than 90°
2) Obtuse – Measures greater than 90° and less than 180°
3) Right – Measures exactly 90°


180
4) Straight – Measures exactly 180° (a straight line, or opposite rays!)
Just like with segments, angles with the same measure are _____________. In pictures, we mark angles
that are ____________. But instead of ______________ , we use _________.
Example: In the picture,  A   B .
This means that m  A  m  B .
A
B
Just as a segment bisector divides a segment into two congruent segments, an _______________________
divides an angle into two congruent angles.
S
Example: In the picture, GW is bisecting  SWA :
G
Name the congruent angles:
W
__________ and ___________
A
N
Example: If FS bisects  NFH , m  NFS  2x 10 , and
m  SFH  x  20 , find m  NFH .
S
F
Example: If m  JKO  4x  2 and m  JKE  9x  22 ,
H
J
find m  EKJ .
O
HOMEWORK:
K
E