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Chapter 3 Student Notes

Chapter 3 Student Notes. Chapter 3 Test Friday, October 12 th. 3.1 Parallel Lines and Transversals. Parallel Lines. A B C D. Skew Lines and Parallel Planes. Two lines are skew if they. l. l and m are ________. m. Examples.

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Chapter 3 Student Notes

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  1. Chapter 3Student Notes Chapter 3 Test Friday, October 12th

  2. 3.1Parallel Lines and Transversals

  3. Parallel Lines A B C D

  4. Skew Lines and Parallel Planes Two lines are skew if they l l and m are ________ m

  5. Examples • Name all segments that are parallel to AD • Name all segments that intersect AD • Name all segments that are skew to AD • Name all planes that are parallel to plane ABC. Answers: • ___________________ • ___________________ • ___________________ • ___________________

  6. Transversal – ___________________________ Exterior Angles – _____________________ Interior Angles – _____________________ • 2 • 3 4 l • 6 • 7 8 m t

  7. 1 2 • 3 4 l m • 5 6 • 7 8 t Consecutive Interior Angles – _____________________ Alternate Exterior Angles – _____________________ Alternate Interior Angles – _____________________ Corresponding Angles – _____________________

  8. q p 1 2 3 4 8 7 6 5 9 10 11 12 16 17 18 19 r Name the transversal that forms each pair of angles. Then name the special name for each pair. s Transversal Special Angle Pair Name • 3 & 11 • 11 & 17 • 17 & 1 • 2 & 3 • 4 & 6 ____ ____ ____ ____ ____ __________________ __________________ __________________ __________________ __________________

  9. 3-2 Angles and Parallel Lines

  10. m If m ║ n , then the following relationships exists: 1 2 3 4 n 5 6 7 8 t

  11. m 1 2 3 4 If m ║ n , then: n 5 6 7 8 t Corresponding ’s  Alternate Interior’s  Alternate Exterior ’s  Consecutive Interior ’s supplementary

  12. If m1 = 70o, find the others. 70o 1 2 3 4 5 6 7 8

  13. If line AB is parallel to line CD and s is parallel to t, find: More Examples 1. The value of x, if m3 = 4x + 6 and m11 = 126. 2. The value of x, if m1 = 100 and m8 = 2x + 10. 3. The value of y, if m11 = 3y – 5 and m16 = 2y + 20.

  14. Important Notes: • When the lines are parallel; • The acute angles ____________________. • The obtuse angles ___________________. • One acute angle is _______________ to one obtuse angle. m 1 2 3 4 n 5 6 7 8 t

  15. 30o 1 36o Find the measure of angle 1.

  16. 140o 1 30o Find the measure of angle 1.

  17. Find the value of x and y. (5y + 10)o (5x)o (10y + 5)o

  18. Find x and y. (8x + 4)0 (6x + 4)0 (6y + 8)0 (5x + 12)0 (2y)0 (5x + 7)0

  19. 3-3 Slopes of Lines

  20. Slope of ǁ, and⊥ lines

  21. Determine if each pair of lines are ǁ , ⊥, or neither. • Line 1, m = -2 • Line 2, m = ½ 2. Line 3, m = 3 Line 4, m = 3 3. Line 5, m = 4/3 Line 6, m = 3/4 4. Line 7, m = -1 Line 8, m = 1

  22. Find the slope of each line. • l • m • Any line ǁ to l. • Any line ⊥ to m. l m

  23. Slope of a Line • The slope of the non-vertical line through the points and is m = The slope of a vertical line ____________. The slope of a horizontal line is _______.

  24. Examples Find the slope of the line through the given points. (-4, 7) and (3, 7)

  25. Examples Find the slope of the line through the given points. (3, -1) and (3, 2)

  26. Examples Find the slope of the line through the given points. (1, -4) and (2, 5)

  27. Examples Find the slope of the line through the given points. (-2, 5) and (1, -1)

  28. Given each pair of points, Determine if AB ǁ CD, AB ⊥ CD, or neither. • A(-3, -2) B(9, 1) C(3, 6) D(5, -2) 2. A(5, -4) B(10, 0) C(9, -8) D(5, -13)

  29. m(l) = m(m) = l m(s) = r s m m(r) =

  30. Graph each line described below. m = 3, passes through (2, 1) Passes through (-4, -5)  the line that passes through MN, M(-1, -3), N(-3, 4) m(MN) = m() =

  31. 3-5 Proving Lines Parallel

  32. Postulate 3-4 If ___________________________________________________ corresponding angles are congruent, then the _________________. , then ______. l if m t

  33. Theorem 3-5 If ________________________________________________________ alternate exterior angles are congruent, then the ___________________. , then ______. l if m t

  34. Theorem 3-6 If __________________________________________________________ consecutive interior angles are supplementary, then ____________________. 1 2 l , then ______. if m t

  35. Theorem 3-7 If ____________________________________________________ alternate interior angles are congruent, then ________________. , then ______. l if m t

  36. Theorem 3-8 l if , then ______. m t

  37. Determine which pair of lines is parallel and why. s r 1.  1   8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 2.  7  12 p q 3.  11  9 4. m 6 +  10 = 180

  38. Find x so thatl|| m (5x +10)o l 110o m

  39. Find x so thatl|| m (6x -10)o l (5x + 15)o m

  40. Find x so thatl|| m l (7x–5)o (5x–7)o m

  41. Find x so thatl|| m (7x–1)o l m

  42. 3.6Perpendiculars and Distance

  43. How would you measure the distance from Fishersville to the Beach? Fishersville Beach

  44. Draw the segment that represents the distance from P to AB. P A B P A B

  45. Draw the segment that represents the distance from P to AB. P P A B A B

  46. Draw the segment that represents the distance from P to AB. A B B P P A

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