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3.4 pgs. 148-154 Theorems about Parallel and Perpendicular Lines Date:
Main Points Questions
Transitive Property of Parallel Lines
If two lines are parallel to the __________ line,
then they are parallel to ____________ _____________.
Linear Pair Perpendicular Theorem
If two lines intersect to form a linear pair of ________________ angles,
then the lines are _________________________ .
Perpendicular Transversal Theorem
In a plane, if a transversal is perpendicular to one of two ____________ lines,
then it is perpendicular to the ____________ __________.
Lines Perpendicular to a Transversal Theorem
In a plane, if two lines are perpendicular to the __________ line,
then they are parallel to ____________ _____________.
Proof Practice Use the diagram to prove Perpendicular Transversal Theorem Given ‖ , , ,
Prove , ,
m n h
1 2 m
n
m
n
t
t m n
A
D
B C
E F
G
H
10 10
Same 99 99 qqeach otherIflinens11h andlinenHeinen thenline millineh
Rightperpendicular 1
If Mcl_900and me2 900 then linen 1 linemo
seifweknowhesarearakeland parallelehavea900 other line 7determineflinesare 1 If dinet 1 line m anddine in Kline n then line t 1 linen
Proveslinesareparallelwhenweknow same
nanglesare each othercongruentBoth90 If line t 1 linen andline t 1 linen then donem 11lineno
statements ReasonsAd 119 Given
93111 GivenMLGBC 900 Def of 1 line
7 MLBEF 900 Corresp 2 spost43ft Def of 1 line
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Name _________________________________________________________ Date _________
In Exercises 3 and 4, determine which lines, if any, must be parallel. Explain your reasoning.
3. 4. 4.
5. Given: 1 2, f h� # � A and ∥
Prove: ∥
In Exercises 2 and 3, determine which lines, if any, must be parallel. Explain your reasoning.
2. 3.
5. Given: 1 2,� # � ∥ and b dA Prove: ∥
6. Find all the unknown angle measures in the diagram. Justify your answer for each angle measure.
3.4 Practice A
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