Download Section 1-4 Angles

Section 1-4: Angles
A. Angle: Formed by two rays with a common
endpoint.
Diagram of an angle.


W
Z
interior
X
exterior
XW and


Y
are the sides of an angle
Sides of an angle are formed by two rays.
XY
X is the vertex because it is the common
endpoint.
*An angle separates a plane in 3 distinct parts:
1. Interior of the angle.
2. Exterior of the angle.
3. Angle itself.
B. Measuring Angles:
1. Protractor: Tool that measures angles
 measured in degrees.
2. Types of Angles:
a.
A is a right angle if mA is 900
A
b.
A is an acute angle if mA is less
than 900
c.
A
A is an obtuse angle if mA is
more than 900 and less than 1800
d.
A is a straight angle if mA is
1800.
3.
A
A
Other Types of Angles:
a.
Congruent Angles: angles that have
equal measure
 Angle measures are equal, but the
angles are congruent
Ex: m 5 = m 6 *m in front of an angle
5  6
means the measure of
the angle
P
R
5
Q
b.
R
Q
S
Adjacent Angles: Two angles in a
plane that have a common vertex
and a common side, but no common
interior points.
P
5
6
6
S
Since 5 and 6 share a
common side, Q R , and a
common vertex, Q, 5
and 6 are adjacent angles.
c. Bisector of an Angle: The ray that
divides the angle into two congruent
adjacent angles.

QR
If
bisects PQS , then
m 5 = m 6 or 5  6
P
R
5
Q
6
S
If m 5 = m 6 , then
bisects PQS .

QR
C. When naming an angle…
a. The vertex must be in the middle
when using 3 points
Ex: PQS  understood Q is the vertex
b. You may name it by its vertex only
if it names exactly one angle
D. Angle Addition Postulate
~ If R lies in the interior of PQS then
MPQR  MRQS  MPQS
~ If MPQR  MRQS  MPQS then R is
in the interior of PQS