Download NAME: 3.2 Properties of Parallel Lines

NAME:___________________ 3.2 Properties of Parallel Lines
Corresponding Angles Postulate:
Find the degree measure of all the
angles. Tell how you got them?
What other angle pair relationships are there?
Alternate Interior Angles Theorem
If a transversal intersects two
parallel lines, then
Same-Side Interior Angles Theorem:
If a transversal intersects two
parallel lines, then
Alternate Exterior Angles Theorem
If a transversal intersects two
parallel lines, then
Ex 1: Find the measures of all of the angles.
Ex 2: Find the measure of each angle indicated.
Ex 3: Solve for x.
Your try:
Summary:
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3.2 Practice Problems
Directions: Identify all the numbered angles that are congruent to the given angle. JUSTIFY your answer.
2)
1)
Directions: Solve for x.
3)
4)
5)
6)
Directions: Find the measure of the angle indicated in bold.
8)
7)
9)
10)
11)
12)
13) Solve for x. Opposite sides of the figure are
parallel.
14) Solve for x. The top and bottom sides are parallel.
Algebra Review
Solve: 2
4
Solve: 15 = 2x - 13
Factor:
14
45
Factor: 16
Graph: 56
6
Graaph:
3
4
3.2 APPLICAT
TION and EX TENSION
DIRE
ECTIONS: SOLVE
S
FOR X.
X
1)
Opposite side
es are paralle
el.
2) O
3) New York City
y’s streets arre laid out in a grid so mo
ost of the st reets all line
e up parallel a
and perpendiicular to each
h
othe
er. However, there are a few streets that go diag
gonally througgh town. The picture below is a repre
esentation of
f
BROADWAY in NYC.
N
It’s a transversal
t
to
o the three parallel stree
ets. Use thiis informatio
on to answer the following
g
questtions.
a) If ∠
42° and W.. 62nd and W.. 61st are parrallel find the
e following:
m∠
m∠
m∠
m
m∠
m∠
m∠
m
b) If ∠
m∠
m∠
42° and W. 62nd is also parallel to W 60th find t he following::
m∠
c) What kind
k
of angle
es are ∠ , ∠ ,
∠ ?
d) If the lines are all parallel
p
then what should be true abo ut all three o
of the
angles? Is
I it true?
4) Spiderman is slinging is way all over NYC. He starts on one building and is going to sling across to the building
opposite which is parallel to the building he is on. He knows that the angle formed between his webbing and the
building (on the bottom side) is 37°. Draw a picture and find the angle that the webbing and building (on the
bottom side form.
5) Write a two-column proof.
Given: ∥ , ∠1 ≅ ∠4
Prove: ∠2 ≅ ∠3