Geometry Section 1.4
Angles and Their Measures
An *angle is the figure formed by
the union of two rays with a
common endpoint.
The rays are called the sides
____ of the
angle and their common endpoint
is the vertex
_____ of
the angle.
The same angle can be named in different ways:
1) by 3 points, with the middle point being the
vertex ABC
2) by just the vertex – must have only one angle
with this vertex
3)
B
The same angle can be named in different ways:
1) by 3 points, with the middle point being the
vertex ABC
2) by just the vertex – must have only one angle
with this vertex
B
3) by using a number placed in the
interior near the vertex
1
Angles are measured using a
__________.
protractor
A common unit used for
degree
measuring angles is the ______.
Note: Radians and gradients are
also used.
We write ______to
mA represent the
measure of  A .
Two angles are congruent iff
their measures are equal.
Tick marks are used to indicate congruent angles
in a figure.
We write ______to
mA represent the
measure of  A .
Postulate 1.3.2: Two angles are
congruent iff their measures are equal.
Tick marks are used to indicate congruent angles
in a figure.
Angles are classified according to their
measure.
An *acute angle is an angle whose
measure is between 0 and 90 degrees.
A *right angle is an angle whose
measure is exactly 90 degrees.
To indicate a right angle
in a figure, place a small
square at the vertex.
Perpendicular lines are two lines that
intersect to form right angles.
To indicate that AB is perpendicular
to CD , we write _________
AB  CD
An *obtuse angle is an angle whose
measure is between 90 and 180 degrees.
A *straight angle is an angle whose
measure is exactly 180 degrees.
The Angle Addition Postulate is similar to
the Segment Addition Postulate.
Postulate 1.3.3: Angle Addition Postulate:
If S is in the interior ofPQR , then
mPQS  mSQR  mPQR
An *angle bisector is the ray which
divides an angle into two
congruent angles.
2 x  8  2 x  8  96  8 x  16
4 x  80  8 x  16
64  4 x
x  16
E
8 x  16
2x  8
96
mDBC  2216  8  2(32  8)  2(24)  48