If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

State the converse.

Lesson 3: Proving Lines are Parallel

'1"ß'lçAlso a Postulate* * *

Given the following information, what can you conclude?

Given: 22 = 13Prcve: I ll m

If two lines are cut by a transversal so that the alternate interior angles are congruent, then thelines are parallel,

Zl=22

If two lines are cut by a transversal so that the alternate exterior angles are congruent, then thelines are parallel.

Given: Zl = 13What can you prove?

If two lines are cut by a transversal so that the consecutive interior angles are supplementary,then the lines are parallel.

Given: 22 and 23 are supplementary

What can you prove?

Given:

Prove:

iilkkll I

i ll I

If two lines are parallel to the same line, then they are parallel to each other.

j

k

I

In a plane if two lines are perpendicular to the same line, then they are parallel to each other,

Given: m a pnap

What can you prove?

SUMMARY

Name 6 ways to prove lines are parallel,

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2. g\^, Êlþra¡

mn

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uwrsr4t,._ f,^+,4ro- ¿ls qß_ sv|plenc.fury

z

Which lines, if any, can be proved parallel from the given information? (TEST QUESTION)

fmø

lM.s

L Zt = Ze sllü2. z5=tt0 tltf3. Z7 = ZIt ¡)o¡. tt

4. 212 = 214 ttl f5, z6 = ze sttË6. sll tandsll u tilv7. z2=zt2 Sttü8. mZl3+mll4:180o tltf9. slwandul-w Slly

û.rL l(

arN- L+o J\. .fq'n c l,¡c

il. Sa*+t¿ ltn.

10.

11.

12.

13.

14.

15.

t2 = Z4 ¡/n- ll

t2 = 23 q-tt ft3 = tt4 6[ltmZ5 + mZ6 +mZ8 : l80o S tl tt3 = Zr2 ¡/anc- [l27 and Zl7 arc supplementu.y Sllt

Given:

Prove:

Zl=2213=24

A-B ll -D

LIL3

St^*.ø ,rrts

2.

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LL 7 t3

3. Lt 7 t4

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4 ED

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f ix.s a'FL I I

l. Given: .lO tt fNZl=12Z3=24

Lesson 3 Practice: Proving Lines are Parallel

JKA

Prove: KO ll AN

Statements

t.

)

3,

4.

5.

6.

7.

Jo ll KN

Zl=23Zl=2222= 13

23=24

Z2=24

Reasons

Ko ll AN

2. Given: Zl = 22

Prove: 23 = 24

5

6

7

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L ? tt t

Statements

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3. L3 ?¿1

+ràr^s *rrJ,

Reasons

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z,

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a-t+.c'^^iL ùt-lcc,'or /t q'la ?'/

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linc a,cc- ll .

ll l¡Ytes a'rL

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Page 160-163 , #7-10,12-29,32,34, 54-57

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