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Geometry Review
Angles and Parallel Lines
Objectives:
Measure and Classify Angles
Describe Angle Pair Relationships
Classify Angle Pairs made by Parallel Lines cut by a
Transversal
Describe Angle Pair Relationships within Parallel Lines
Part 1: Angles
Vertex
An angle consists of two
A
Sides
B
different rays (sides) that
share a common endpoint
(vertex).
C
This angle can be called: Angle ABC, <ABC, <CBA
OR it can be named by the vertex like so: <B
Types of Angles
Go to the following website to learn about the different types of angles.
Don’t forget to press the play button on top of the picture to see the animation.
http://www.mathsisfun.com/angles.html
Use the diagram to find the measure of the indicated
angle. Then classify each angle as either acute, right,
obtuse, or straight.
1. KHJ
2. GHK
3. GHJ
4. GHL
5.
What is the measure of
DOZ?...
How did you get to your
answer?
D
G
25
O
40
Z
Angle Addition Postulate
If P is in the interior of RST, then mRST =
mRSP + mPST.
6.
Given that mLKN = 151°, find
mLKM and mMKN.
M
L
2x+10
4x-3
K
N
Congruent Angles
Two angles are congruent angles if
they have the same measure.
Angle Bisector
An angle bisector is a ray
that divides an angle into
two congruent angles.
7.
Ray BD bisects <ABC.
Solve for x.
B
A
D
( x 2  21)o
(10 x )
C
8.
In a diagram, YW bisects XYZ. mXYW = (m2  81) °
and m ZYW= (-18m)°. Find mXYW.
Hint: Draw the picture
Hint: Angle may not be drawn to scale
C Comes Before S…
Complementary Angles Sum to 90 Degrees
Supplementary Angles Sum to 180
m1  m2  90
m3  m4  90
m5  m6  180
m7  m8  180
Linear Pairs of Angles
Linear Pairs of Angles
Two adjacent angles
form a linear pair if
their noncommon sides
are opposite rays.
The angles in a linear
pair are
supplementary.
Vertical Angles
Vertical Angles
Two nonadjacent angles
are vertical angles if
their sides form two
pairs of opposite rays.
Vertical angles are
formed by two
intersecting lines.
S
9. Name a pair of complementary
10.
11.
12.
13.
angles.
Name a pair of supplementary
angles.
Y
Name a linear pair.
Name a pair of vertical angles.
Name a pair of congruent
angles.
U
T
X
W
V
Part 2: Parallel Lines
What would you call two lines which do not intersect?
Answer: Parallel Lines
Exterior
B
A
Interior
D
C
Exterior
A solid arrow placed
on two lines of a
diagram indicate the
lines are parallel.
The symbol || is used to
indicate parallel lines.
AB || CD
A slash through the parallel symbol || indicates the
lines are not parallel.
B
AB || CD
A
D
C
Transversal
Definition: A line, ray, or segment that intersects 2
or more COPLANAR lines, rays, or segments.
Exterior
Exterior
Parallel
lines
Interior
Non-Parallel
lines
Interior
Exterior
Exterior
transversal
transversal
Transversal A transversal is a line which intersects two or
more lines in a plane. The intersected lines do
not have to be parallel.
j
k
m
t
Lines j, k, and m are
intersected by line t.
Therefore, line t is a
transversal of lines
j, k, and m.
INTERIOR
–The space INSIDE the 2 lines
interior
EXTERIOR
-The space OUTSIDE the 2 lines
In the diagram below:
Angles 1, 2, 7 and 8 are
exterior angles.
Angles 3, 4, 5, and 6 are on
the interior.
exterior
Exterior
1
exterior
3
2
4
Interior
5 6
7 8 Exterior
When two parallel lines are cut by a transversal
special angle relationships form.
Exterior
1
3 4
Interior
5 6
7 8
Exterior
2
♥Alternate Interior Angles
are CONGRUENT
♥Alternate Exterior Angles are
CONGRUENT
♥Same Side Interior Angles are
SUPPLEMENTARY
♥Same Side Exterior Angles are
SUPPLEMENTARY
Corresponding Angles
Corresponding Angles: Two angles that occupy
corresponding positions.
 2   6,  1   5,  3   7,  4   8
Exterior
1
3
2
4
Interior
5 6
7 8 Exterior
Corresponding Angles
When two parallel lines are cut by a transversal, pairs of
corresponding angles are formed.
L
Line L
GPB = PQE
G
A
D
P
B
Q
E
F
Line M
Line N
GPA = PQD
BPQ = EQF
APQ = DQF
Four pairs of corresponding angles are formed.
Corresponding pairs of angles are congruent.
Lines l and m are parallel. l||m.
14. Name all pairs of corresponding angles.
15. Determine all the missing angle
measures.
42°
c°
a°
b°
d°
e°
g°
f°
l
m
Same Side Interior/Exterior Angles
Same Side Interior Angles: Two angles that lie between parallel
lines on the same sides of the transversal.
APQ + DQP = 1800
Same Side Exterior Angles: Two angles that lie outside parallel
lines on the same sides of the transversal.
L
A
G
Line L
1200
Exterior
P
B
600
1200
600
D
BPQ + EQP = 1800
Interior
E
Q
F
Line M
Exterior
Line N
Same Side Interior or
Same Side Exterior
angles are
supplementary.
Alternate Interior/Exterior Angles
Alternate Interior Angles: Two angles that lie between parallel
lines on opposite sides of the transversal (but not a linear pair).
Alternate Exterior Angles: Two angles that lie outside parallel
lines on opposite sides of the transversal.
L
G
A
D
Line L
P
B
Q
E
Line M
Line N
BPQ = DQP
APQ = EQP
F
Two pairs of alternate angles are formed.
Lines l and m are parallel. l||m
16. Name all pairs of alternate interior angles.
17. Name all pairs of alternate exterior angles.
18. Determine all the missing angle measures.
81°
c°
a°
b°
d°
e°
g°
f°
l
m
Make sure you are in slide show view to do this test. Name the
pairs of the following angles formed by a transversal.
GG
G
AA
500
Line
Line
Line LL
L
P P
BBB
1300
D
DD
Q
Q
Q
EEE
FFF
Line
Line
Line
MM M
Line
Line
N
Line
NN
19) Find the missing angles.
70 °
70 °
b°
Hint: The 3 angles in a
triangle sum to 180°.
d°
65 °
20) Find the missing angles.
45 °
50 °
b°
Hint: The 3 angles in a
triangle sum to 180°.
d°
75 °
In the figure a || b.
21. Name the angles congruent to 3.
22. Name all the angles supplementary to 6.
23. If m1 = 105° what is m3?
24. If m5 = 120° what is m2?
25. Final Exercise
40°
60°
Find all the missing
angle measures,
and name the
postulate or
theorem that
gives us
permission to
make our
statements.