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Section 3.1 ~ Parallel and Skew lines!

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1 Section 3.1 ~ Parallel and Skew lines!
Be able to identify angle pairs (corresponding, alternate interior, same-side interior, alternate exterior, same-side exterior)! Quick Definitions: Parallel lines: coplanar lines that do not intersect Parallel planes: planes that do not intersect Skew lines: noncoplanar lines that do not intersect

2 A transversal is a _____ that intersects two other ______!
line A transversal is a _____ that intersects two other ______! lines t In this picture, line ____ is the transversal. 1 2 3 4 n 8 5 This transversal creates ____ angles! 6 7 8 m Pairs of these angles have special names, depending on their positions. t

3 Identify the transversal(s) in each picture:
b c k m n r s t p line m line b lines s, t, p, r

4 Special Angle Pairs in Parallel Lines Cut by a Transversal:
Picture: Relationship: Corresponding Angles Alternate Interior Angles Consecutive Interior Angles Alternate Exterior Angles Consecutive Exterior Angles congruent congruent supplementary congruent supplementary

5 Practice Identifying the Special Angle Pairs:
Corresponding Angles Alternate Interior Angles Consecutive Interior Angles Alternate Exterior Angles Consecutive Exterior Angles 1 & 5, 4 & 8, 2 & 6, 3 & 7, 1 & 9, 2 & 10, 4 & 12, 3 & 11 1 2 3 4 5 6 7 8 9 10 11 12 4 & 6, 3 & 5, 2 & 12, 3 & 9 4 & 5, 3 & 6, 2 & 9, 3 & 12 1 & 7, 2 & 8, 1 & 11, 4 & 10 1 & 8, 2 & 7, 1 & 10, 4 & 11

6 Use the picture to complete each statement:
50 If m5 = 130, then m8 =____ because they are… 1 2 3 4 5 6 7 8 9 10 11 12 supplementary 125 If m4 = 125, then m6 =____ because they are… alternate interior 125 If m4 = 125, then m8 =____ because they are… corresponding 135 If m2 = 45, then m7 =____ because they are… consecutive ext 130 If m3 = 50, then m6 =____ because they are… consecutive int 42 If m7 = 42, then m1 =____ because they are… alternate ext

7 MORE PRACTICE: Use the picture to complete each statement.
50 If m5 = 130, then m4 =____ because they are… 1 2 3 4 5 6 7 8 9 10 11 12 same-side interior 25 If m5 = 25, then m3 =____ because they are… alternate interior 125 If m5 = 125, then m1 =____ because they are… corresponding 130 If m1 = 50, then m8 =____ because they are… same-side ext 130 If m3 = 50, then m2 =____ because they are… supplementary 51 If m2 = 51, then m8 =____ because they are… alternate ext

8 Find the value of each variable.
2x 2x + 60 x + 60 3x - 20 2x + 2x + 60 = 180 3x - 20 = x + 60 4x + 60 = 180 2x - 20 = 60 4x = 120 2x = 80 x = 30 x = 40

9 Your Turn! 60° 3y 3y + 60 = 180 3y = 120 y = 40


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