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Jim Smith JCHS Jim Smith JCHS Section 3-1, 3-2 Section 3-1, 3-2

3 1, 3-2 parallel lines & transversals

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Page 1: 3 1, 3-2 parallel lines & transversals

Jim Smith JCHSJim Smith JCHSSection 3-1, 3-2Section 3-1, 3-2

Page 2: 3 1, 3-2 parallel lines & transversals

A Line That Intersects 2 Or MoreA Line That Intersects 2 Or MoreLines At Different Points Is Lines At Different Points Is

Called A Transversal Called A Transversal

transverstransversalal

Page 3: 3 1, 3-2 parallel lines & transversals

When This Happens,When This Happens, 8 Angles Are Formed8 Angles Are Formed

11

22

33

44

55

66

77

88

Page 4: 3 1, 3-2 parallel lines & transversals

11

223344

55

6677

88

This Forms 2 NeighborhoodsThis Forms 2 Neighborhoods

Page 5: 3 1, 3-2 parallel lines & transversals

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RememberRememberVertical And Linear AnglesVertical And Linear Angles

VerticalVertical

Page 6: 3 1, 3-2 parallel lines & transversals

Linear PairsLinear Pairs

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44

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Page 7: 3 1, 3-2 parallel lines & transversals

11 33 55 77

22 44 66 88

These Angles AreThese Angles AreCalled Called

ConsecutiveConsecutiveOr Same Side Or Same Side

AnglesAngles

Page 8: 3 1, 3-2 parallel lines & transversals

3344

55

66

11

2277

88

Interior Interior AnglesAngles

(Between 2 lines)(Between 2 lines)

Exterior AnglesExterior Angles ((outside the lines)outside the lines)

Page 9: 3 1, 3-2 parallel lines & transversals

Alternate Angles Are On Alternate Angles Are On Different Sides Of The Different Sides Of The

TransversalTransversalAnd And From Different From Different

NeighborhoodsNeighborhoods1122

3344

5566

7788

Alternate ExteriorAlternate ExteriorAngles 1 And 8Angles 1 And 8Angles 2 And 7Angles 2 And 7

Alternate InteriorAlternate InteriorAngles 3 And 6Angles 3 And 6Angles 4 And 5Angles 4 And 5

Page 10: 3 1, 3-2 parallel lines & transversals

11

33 55

77

22

44 66

88

Consecutive Consecutive IntIntAngles 3 and Angles 3 and 55Angles 4 and Angles 4 and 66

Consecutive ExtConsecutive ExtAngles 1 and 7Angles 1 and 7Angles 2 and 8Angles 2 and 8

Page 11: 3 1, 3-2 parallel lines & transversals

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Corresponding Angles Are Corresponding Angles Are Located In The Same Position Located In The Same Position

In Each NeighborhoodIn Each Neighborhood

Page 12: 3 1, 3-2 parallel lines & transversals

1111 1212

1313 1414

1515 116617171818

Name The Name The AnglesAngles1.1. 11 and 11 and

15152.2. 12 and 12 and 1616

3.3. 13 and 13 and 1616

4.4. 12 and 12 and 1818

5.5. 14 and 14 and 1616

6.6. 14 and 14 and 1818

7.7. 11 and 11 and 1414

8.8. 15 and 15 and 17 17

Page 13: 3 1, 3-2 parallel lines & transversals

1.1.CorrespondingCorresponding2.2.CorrespondingCorresponding3.3.Alt InteriorAlt Interior4.4.Consecutive (SS) ExteriorConsecutive (SS) Exterior5.5.Consecutive (SS) InteriorConsecutive (SS) Interior6.6.CorrespondingCorresponding7.7.VerticalVertical8.8.Linear Linear

Page 14: 3 1, 3-2 parallel lines & transversals

11 2233 44

55 66 77 88

99 1010 11111212

1313 1414 1515 1616

With This Diagram, We Can Work With This Diagram, We Can Work With Angles In Different With Angles In Different Neighborhoods As LongNeighborhoods As LongAs They Are Connected By A As They Are Connected By A TransversalTransversal

Name the anglesName the angles

1.1. 1 and 31 and 32.2. 7 and 127 and 123.3. 11 and 1411 and 144.4. 6 and 106 and 105.5. 13 and 513 and 56.6. 9 and 69 and 67.7. 1 and 131 and 138.8. 5 and 45 and 49.9. 7 and 117 and 1110.10. 6 and 116 and 11

Page 15: 3 1, 3-2 parallel lines & transversals

1.1. CorrespondingCorresponding2.2. Alt. Int.Alt. Int.3.3. Alt. Int.Alt. Int.4.4. Cons. (SS) Int.Cons. (SS) Int.5.5. CorrespondingCorresponding6.6. Alt. Int.Alt. Int.7.7. Consecutive Consecutive

ExtExt8.8. Alt. ExtAlt. Ext9.9. Cons. (SS) Int.Cons. (SS) Int.10.10.NoneNone

Page 16: 3 1, 3-2 parallel lines & transversals
Page 17: 3 1, 3-2 parallel lines & transversals

If 2 Parallel Lines Are Cut By A If 2 Parallel Lines Are Cut By A Transversal Then:Transversal Then:

Corresponding AnglesCorresponding Angles Are CongruentAre Congruent

Alternate InteriorAlternate InteriorAngles Are CongruentAngles Are Congruent

Same Side Interior Angles Same Side Interior Angles Are SupplementaryAre Supplementary

Page 18: 3 1, 3-2 parallel lines & transversals

Remember ………Even Without Parallel

Lines

Vertical Angles Are Always Congruent

Linear Pairs Are Always Supplementary

Remember ………Even Without Parallel

Lines

Vertical Angles Are Always Congruent

Linear Pairs Are Always Supplementary

Page 19: 3 1, 3-2 parallel lines & transversals

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aa

bb

a b a b m 1 = m 1 = 105105

Find:Find:1.1. 3 = 3 = 2.2. 6 =6 =3.3. 7 =7 =4.4. 4 =4 =5.5. 5 =5 =

757575757575105105105105

Page 20: 3 1, 3-2 parallel lines & transversals

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33 44

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aa

bb63°63°

117°117°

119°119°

119119°°

119°119°

119°119°

61°61°

63°63°

63°63°

Page 21: 3 1, 3-2 parallel lines & transversals

a b a b 2x+62x+6

3x-103x-105x-205x-20

2x-102x-10

2x+6 = 3x-102x+6 = 3x-10 6 = x – 106 = x – 10 16 = x16 = x

5x-20+2x-10 = 1805x-20+2x-10 = 180 7x-30 = 1807x-30 = 180 7x = 2107x = 210 x = 30x = 30

4x+254x+25

6x-156x-15

4x+25 = 6x-154x+25 = 6x-15 25 = 2x-1525 = 2x-15 40 = 2x40 = 2x 20 = x20 = x