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HW-3.3 Practice B (1-8)
3.1-3.3 Quiz THU 10-23
www.westex.org HS, Teacher Websites
10-20-14
Warm up—Geometry CPA
Line h and line j are parallel. Find all the
missing angles.
49o 2
3 4
h
5
6
7 8
j
GOAL:
I will be able to:
1. use the angles formed by a transversal to prove
two lines are parallel.
HW-3.3 Practice B (1-8)
3.1-3.3 Quiz THU 10-23
www.westex.org
HS, Teacher Websites
Name _________________________
Date ________
Geometry CPA
3.3 Proving Lines Parallel
GOAL:
I will be able to:
1. use the angles formed by a transversal to prove two lines are parallel.
The converse of a theorem is found by exchanging the _______________ and
_______________. The converse of a theorem is not automatically true. If it is true, it
must be stated as a ______________ or ______________ as a separate theorem.
Example 1: Using the Converse of the Corresponding Angles Postulate
Use the Converse of the Corresponding Angles Postulate and the given information to
show that ℓ || m.
4  8
4  8
_________________________
ℓ || m
_________________________
You Try:
Use the Converse of the Corresponding Angles Postulate and the given information to
show that ℓ || m.
1  3
1  3
__________________________
ℓ || m
__________________________
Example 1B: Using the Converse of the Corresponding Angles Postulate
Use the Converse of the Corresponding Angles Postulate and the given information to
show that ℓ || m.
m3 = (4x – 80)°,
m7 = (3x – 50)°, x = 30
m3 = 4(30) – 80 = 40o
_________________________
40o = 3(30) – 50 = m7
_________________________
_______________
_________________________
_______________
_________________________
ℓ || m
_________________________
You Try:
Use the Converse of the Corresponding Angles Postulate and the given information to
show that ℓ || m.
m7 = (4x + 25)°,
m5 = (5x + 12)°, x = 13
m7 = 4(13) + 25 = 77o
_________________________
77o = 5(13) + 12 = m5
_________________________
_______________
_________________________
_______________
_________________________
ℓ || m
_________________________
Example 2: Determining Whether Lines are Parallel
Use the given information and the theorems you have learned to show that r || s.
4  8
4  8
_______________
r || s
_______________
You Try
Use the given information and the theorems you have learned to show that r || s.
2  6
2  6
_______________
r || s
_______________
Example 2B: Determining Whether Lines are Parallel
Use the given information and the theorems you have learned to show that r || s.
m2 = (10x + 8)°, m3 = (25x – 3)°, x = 5
m2 = 10x + 8 = 10(5) + 8 = 58o
_______________
m3 = 25x – 3 = 25(5) – 3 = 122o
_______________
m2 + m3 = 58° + 122° = 180o
_______________
r || s
_______________
You Try:
Use the given information and the theorems you have learned to show that r || s.
m3 = 2x, m7 = (x + 50), x = 50
m3 = 2x = 2(50) = 100°
_______________
100°= x + 50 = (50) + 50 = m7 _______________
m3 = m7
_______________
3  7
_______________
r || s
_______________
Example 3: Proving Lines Parallel
Given: p || r , 1  3
Prove: ℓ || m
FIND THE TYPO IN THE PICTURE!!!