21
Section 4.1 & 2 Section 4.1 & 2
Section 4.1 & 2Section 4.1 & 2
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
When This Happens,When This Happens, 8 Angles Are Formed8 Angles Are Formed
11
22
33
44
55
66
77
88
11
223344
55
6677
88
This Forms 2 NeighborhoodsThis Forms 2 Neighborhoods
11
22
33
44
55
66
77
88
RememberRememberVertical And Linear AnglesVertical And Linear Angles
VerticalVertical
Linear PairsLinear Pairs
11
22
33
44
55
66
77
88
11 33 55 77
22 44 66 88
These Angles AreThese Angles AreCalled Called
ConsecutiveConsecutiveOr Same Side Or Same Side
AnglesAngles
3344
55
66
11
2277
88
Interior Interior AnglesAngles
(Between 2 lines)(Between 2 lines)
Exterior AnglesExterior Angles ((outside the lines)outside the lines)
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
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
11
22
33
44
55
66
77
88
Corresponding Angles Are Corresponding Angles Are Located In The Same Position Located In The Same Position
In Each NeighborhoodIn Each Neighborhood
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
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
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 13
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
ExtExt
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
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
11 22
33 44
55 66
77 88
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
11 22
33 44
55 66
77 88
aa
bb63°63°
117°117°
119°119°
119119°°
119°119°
119°119°
61°61°
63°63°
63°63°
Assignment
• TB p144: 2-20 even
• TB p152: 20-38 even
