Download Geometry Notes

Geometry Notes
Lesson 1.3A – Angles
LG.1.G.4
Apply, with and without appropriate technology,
definitions, theorems, properties, and postulates
related to such topics and complementary,
supplementary, vertical angles, linear pairs, and angles
formed by perpendicular lines.
Angle
The figure formed by two rays with
a common endpoint.
side
vertex
side
Three ways to name an angle:
1.
2.
3.
The vertex (only
when there is one
angle at the vertex)
Three letters
(vertex is always
the middle letter)
A number
Angle Addition Postulate
If D is in the interior of
ABC, then
m ABD + m DBC = m ABC
A
B
D
C
Example…
Given m ABD = 45°
m DBC = 32°
m ABC = _____________
A
B
D
C
Now You Try…
m SQT = _________
S
m PQR = _________
m SQP = _________
R
25°
Q
T
50°
43°
P
Types of Angles
Vertical Angles –
nonadjacent angles
formed by two
intersecting lines
X
Y
O
Name a pair of vertical
angles.
Look at the size
(measurement) of one
pair of vertical angles.
What might you guess
about their
measurements?
Z
W
Now You Try…
Name a second angle in
each pair of vertical
angles.
C
 EOD
 BOC
F
 EOB
A
E
O
D
B
Types of Angles (cont.)
Supplementary Angles – two
angles, whose sum of their
measures equals180°
105O
75O
C
D
Angles C and D are
supplementary.
Example…
x=
120o
xo
Types of Angles (cont.)
Complementary Angles – two
angles, whose sum of their
measures equals 90°
50O
A
40o
B
Angles A and B are
complementary.
Example. . .
y=
yo
25o
Example . . .
Given: KLM is a right angle.
If
2. If
3. If
4. If
1.
m  KLP = 57°, find mMLP.
m MLP = 69°, find mKLP.
mNPM = 120°, find m MPL.
mKPL = 130°, find m KPN
K
L
P
N
M
Now you try. . .
Given:  BAD is a right angle.
If
2. If
3. If
4. If
1.
m BAE = 74°, find m EAD.
m  EAD = 36°, find m  BAE.
mCED = 71°, find m  CEB.
m  AED = 117°, find m  BEA.
B
C
E
A
D