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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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