Download 3.1: Parallel Lines - msstarnes-math

Tuesday, February 12th
1) Simplify: 3x + 5(9x + 4) - 10
2) The coordinates of the
endpoints of the diameter of a
circle are H (5, -1) and K (-9, 13).
What are the coordinates of the
center of the circle?
3) If OF bisects ∡COP, what angles
have to be congruent?
Answers to Triangle Wks.
1) 75
9) 29
2) 63
10) 147
3) 20
11) 60
4) 55
12) 27
5) 23
13) 50
6) 17
14) 130
7) 85
15) 112
8) 30
16) 32
17) 22
18) 120
19) 31
20) 65
21) 112
22) 68
23)90
24) 90
25) 22
26) 158
Parallel Lines
Vertical Angles  two angles whose sides form two pairs
of opposite rays (make an X)
 vertical angles are congruent
1
4
3
2
Example: Find the value of x.
a)
(2x + 3)o
(4x -101)o
Transversal  Line that intersects two coplanar
lines at two distinct points
transversal
Corresponding Angles  Formed by the intersection of two
coplanar lines and a transversal
 Angles that are in the same spot at
each location
1
3
2
4
Alternate Interior Angles  Formed by the intersection of two
coplanar lines and a transversal
 Inside parallel lines and on opposite
sides of transversal
5
8
7
6
Same-Side Interior  Formed by the intersection of two
coplanar lines and a transversal
 On the inside of the parallel lines and
on the same-side on the transversal
9
11
10
12
Example: Identify the following
angles as corresponding, alternateinterior, or same-side interior.
Name the transversal.
a) Angles 10 and 16
b) Angles 1 and 9
Example: Identify the following
angles as corresponding, alternateinterior, or same-side interior.
Name the transversal.
c) Angles 8 and 11
d) Angles5 and 13
Play-doh Activity
 Work with your partner and
complete the worksheet.
 When you are done, make sure I
check your paper.
 Homework: Parallel Lines
Worksheet
ONLY IF LINES ARE
PARALLEL…
Alternate-interior angles
are congruent
Same-side interior are
supplementary
Corresponding angles are
congruent
1 5
6
2
n
3
m
Example: Find the measure of
each angles given that m ll n and
that angle 2 measures 50o
a) 1 
7
4
8
b) 3 
c) 4 
d) 5 
e) 6 
f) 7 
g) 8 
Example: Find the values of
a, b, and c
a b c
65o
40o
Example: Find the values of x
and y
xo
50o
yo
70o
Example: Find the values of x
and y. Then find the measures
of the angles.
(2x)o
90o
yo
(y – 50)o
Tuesday, September 11
Have your homework
out!
Book p. 121 #37-41
Proving Lines
Parallel
Converse of the Corresponding
Angles Postulate
If two lines are cut by a
transversal and congruent
corresponding angles, then the
two lines are parallel.
Flow Proof
 arrows show the logical connectors
between the statements
Proof of Converse AlternateInterior Angles
Given:
Prove: l ll m
3
2
1
l
m
Converse of the AlternateInterior Angles Theorem
If two lines are cut by a
transversal and congruent
alternate-interior angles, then
the two lines are parallel.
Converse of Same-side
Interior Angles Theorem
If two lines are cut by a
transversal and supplementary
same-side interior angles, then
the two lines are parallel.
Example: Identify which lines must
be parallel if the following angles
are congruent. Justify your answer
with a theorem or postulate.
a) Angles 10 and 16
b) Angles 1 and 9
Example: Identify which lines must
be parallel if the following angles
are congruent. Justify your answer
with a theorem or postulate.
c) Angles 8 and 11
d) Angles5 and 13
E
Given : a ll b
Prove: 4  8
2
1
A
3
7
4
6
5
C
8
F
a ll b
given
B
4  8
If parallel lines are
cut by a transversal,
then corresponding
angles are congruent.
D
Given: AB ll CD
Prove: 2  7
E
2
1
A
3
6
5
C
7
F
8
B
4
D
Given: 1  2
Prove: m ll n
p
1
Statement
m
Reason
1  2
given
m ll n
2
n
If two lines are cut by a
transversal and
corresponding angles are
congruent, then the lines
are parallel
Given:5 and 3 are supplementary
Prove: AB ll CD
Statement
Reason
Given: r  p, t  p
Prove: r ll t
1
p
r
Statement
Reason
2
t
Theorem 3.5
If two lines are parallel to
the same line, then they
are parallel to each other.
Theorem 3.6
 In a plane, if two lines are
perpendicular to the same
line, then they are parallel
to each other.
Example: Find the value of
x for which l ll m.
(14 + 3x)o
(5x – 66)o
Example: Find the value of
x for which l ll m.
(7x – 8)o
62o
Class Work
Proof Stations
Homework:
Finish Proof
Worksheet
48)
Wednesday, September 12th
1) Simplify: 3x + 5(9x + 4) - 10
2) The coordinates of the
endpoints of the diameter of a
circle are H (5, -1) and K (-9, 13).
What are the coordinates of the
center of the circle?
3) If OF bisects ∡COP, what angles
have to be congruent?
POP QUIZ 
Angle Type
Vertical
Corresponding
Same-side
interior
Alternate
interior
What
What else
letter do
do you
they form?
know?
On the Back of Your Quiz
Rate your partners
from today!
Example: Joe – 95
because he worked hard
Sue – 50 because she only
did half of the stations
Class Work
Proof Stations