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HW-3.3 Practice B (1-8)
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10-17-14
Warm up—Geometry H
Finish the conditional statement below so that it
is true and then write the converse of it.
If two lines that are cut by a transversal are
parallel then corresponding angles are _________.
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)
www.westex.org
HS, Teacher Websites
Name _________________________
Date ________
Geometry Honors
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 HYPOTHESIS and CONCLUSION. The
converse of a theorem is not automatically true. If it is true, it must be stated as a
POSTULATE or PROVEN 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
Angle 4 and angle 8 are corr. angles
ℓ || m
CONVERSE of corr. angles postulate
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
substitution
40o = 3(30) – 50 = m7
substitution
m3 = m7
transitive prop of equality
3  7
Definition of  angles
ℓ || m
Converse of corr. angles postulate
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
_________________________
The PARALLEL POSTULATE guarantees that for any line ℓ, you can always construct a parallel
line through a point that is not on ℓ.
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
4 and 8 are alt. ext. s
r || s
Converse of alt. ext. s thm.
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
substitution
m3 = 25x – 3 = 25(5) – 3 = 122o
substitution
m2 + m3 = 58° + 122° = 180o
2 & 3 are same side int. s
r || s
Conv. of same side int. s thm.
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°
_______________
m7 = x + 50 = (50) + 50 = 100° _______________
3  7
_______________
r || s
_______________
Example 3: Proving Lines Parallel
Given: p || r , 1  3
Prove: ℓ || m
SEE the TYPO in PIC?
You Try:
Given: 1  4, 3 and 4 are supplementary.
Prove: ℓ || m