The document introduces several key concepts about angles: 1) It defines an angle as the union of two rays with a common endpoint called the vertex. 2) It classifies angles as acute, right, or obtuse based on their measure. 3) It defines congruent angles, adjacent angles, and a linear pair of angles. 4) It introduces the angle bisector, angle addition postulate, and linear pair postulate as tools for working with angles.

1. It’s All About the
Angles
…in Section 1-4…

2. First, Some New Definitions
Angle – the union of two distinct rays with a
common endpoint
Vertex – common endpoint of the 2 rays of an angle
D• Notation:
DCE ECD
OR OR
1
C
• 1 C
E
What is the vertex of this angle? Point C!

3. Several Classifications of Angles
L V
T P
O
Acute Angle – measures between 0 and 90
Example: VOL
Right Angle – measures 90
Example: LOP
Obtuse Angle – measures between 90 and 180
Example: POT

4. More New Definitions
Congruent Angles – angles that have equal measures
1= 2
2
1 m 1=m 2
Adjacent Angles – two angles in a plane that have a
common vertex and a common side but no common
interior points
L• V Which angles are
• adjacent, and which
T angles are not?
• P
O •

5. More New Definitions
Linear Pair – two adjacent angles that form a
straight line
1 2
1 and 2 are a linear pair

6. More New Definitions
Angle Bisector – a ray that divides an angle
into two congruent adjacent angles
A
•
If 1= 2, then
1 B
Y •
2 YB is an angle bisector
C•

7. Some New Tools
Angle Addition Postulate (AAP) – If B lies in
the interior of AOC, then
m AOB + m BOC = m AOC
C
•
B
•
A
• O

8. Some New Tools
Linear Pair Postulate (LPP) – If AOC is a straight
angle, and B is any point not on AC, then
m AOB + m BOC = 180
B
•
• •
A O C