1.4 Angles and Measures
Angle Addition Postulate
Classify angles
Definition of an angle
Two rays that have the same initial point
called the Vertex
Named ∠ABC
A
All angles are named
with three letters.
B
The middle letter is
the vertex.
C
Angle Measure
We use a protractor to measure angles and is
given a letter m before the name when standing
for its measure.
m∠ABC = 50ᵒ, so the angle has a measurement of
50 degrees.
The Protractor Postulate
like the Ruler postulate for angles
• The measure of an angle is the absolute value of
the different of the terminal side and the initial
side.
X
terminal side
50 ᵒ
Y
Initial side
Z
Angles can be also be Congruent
Again the definition of Congruent is
Same Shape and Same Size.
If m∠XYZ = m∠ABC, then ∠XYZ≌∠ABC.
If ∠PQR≌∠FMB, then ∠PQR≌∠BMF,
but not ∠PQR≄∠MBF. Order is important!
The vertex must be in the middle
Angles have an Interior and an Exterior
K
Q
Interior
Exterior
X
The Angle Addition Postulate
If P is in the interior of ∠RST,
then m∠RSP + m∠PST = m∠RST
T
m∠TSP = 12ᵒ
P
m∠PSR = 24ᵒ
S
R
m∠RST = 36ᵒ
Classifying Angles
Acute
0 to less then
90ᵒ degrees
Right
90ᵒ degrees
Straight Angle equals 180ᵒ
Obtuse
More then
90ᵒ degrees
Adjacent Angles
Adjacent means next to each other; the same as
adjacent lockers. Adjacent lockers share one
wall.
Adjacent angles share one side and have a
common vertex.
∠ABC and ∠CBX are
A
C
adjacent angles
B
X
Homework
Page 29 – 31 #17 – 22, 26- 34, 38, 41, 42, 51-53