Download Section 1.4 - Angles and Their Measures

Section 1.4 - Angles and Their Measures
*Watch this video to give you a better grasp of the concepts listed below.*
Angle: consists of two different rays that have the same initial point.
A
Vertex: The point where the two rays intersect. Point B
B
Sides: The two rays that form the angle.
.
and
.
.C
Name (notation): How we refer to an angle.
or
or
*If there are multiple angles from the same vertex then the angle has to be named by three points.
The vertex is always listed in the middle of the angle name.
Example 1: Name the angles in this figure:
Classifying Angles:
Type
Definition
Acute
Angle measure between 0· and 90·
Obtuse
Angle measure between 90·and 180·
Right
Angle measure of 90·
Straight
Angle measure of 180·
Picture
Congruent Angles: angles that have the same measure.
Measures are Equal
Angles are Congruent
(numbers)
(angles/picture)
Postulate 3: Protractor Postulate
The measure of
is equal to the absolute value of the difference between the real numbers for
and
Interior of an angle: all points between the points that lie on each side of the angle.
(Inside the angle)
Exterior of an angle: all points not on the angle or in its interior. (Outside the angle)
Adjacent angles: two angles that share a common vertex and side, but have no common interior points.
Pairs of adjacent angles:
Postulate 4: Angle Addition Postulate (AAP)
If is in the interior of
, then
.
Example 2: Use the following info to make a sketch, and then answer the questions.
Q is in the interior of
S is in the interior of
P is in the interior of
a) Find
b) Find
c) Find
Example 3: Draw
Given
with point E in the interior of the angle.
, and
d) Find
*Watch this video to see the examples worked through*