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.
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
