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

2. 3.1 Parallel Lines and Transversals

3. Parallel Lines AB C D

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

5. Examples 1. Name all segments that are parallel to AD 2. Name all segments that intersect AD 3. Name all segments that are skew to AD 4. Name all planes that are parallel to plane ABC. Answers: 1. ___________________ 2. ___________________ 3. ___________________ 4. ___________________

6. t Transversal – ___________________________ Exterior Angles – _____________________ Interior Angles – _____________________ l m 12 3 4 5 6 7 8

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

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

10. 3-2 Angles and Parallel Lines

11. 1 2 3 4 5 6 7 8 m n t If m ║ n, then the following relationships exists:

12. 1 2 3 4 5 6 7 8 m n t If m ║ n, then: Corresponding  ’s  Alternate Interior  ’s  Alternate Exterior  ’s  Consecutive Interior  ’s supplementary

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

14. More Examples 1. The value of x, if m  3 = 4x + 6 and m  11 = 126. If line AB is parallel to line CD and s is parallel to t, find: 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.

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

16. 1 30 o 36 o Find the measure of angle 1.

17. 1 140 o 30 o Find the measure of angle 1.

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

19. (5x + 7) 0 (8x + 4) 0 (2y) 0 (5x + 12) 0 (6y + 8) 0 (6x + 4) 0 Find x and y.

21. 3-3 Slopes of Lines

22. Slope of ǁ, and ⊥ lines

23. Determine if each pair of lines are ǁ, ⊥, or neither. 1.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

24. Find the slope of each line. 1. l 2. m 3.Any line ǁ to l. 4.Any line ⊥ to m. l m

25. 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 _______.

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

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

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

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

30. Given each pair of points, Determine if AB ǁ CD, AB ⊥ CD, or neither. 1.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)

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

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

34. 3-5 Proving Lines Parallel

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

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

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

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

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

40. Determine which pair of lines is parallel and why. 1 2 3 4 5 67 8 9 10 11 12 13 14 15 16 p q rs 1.  1   8 2.  7   12 3.  11   9 4. m  6 +  10 = 180

41. Find x so that l || m 110 o (5x +10) o l m

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

43. Find x so that l || m (5x–7) o (7x–5) o l m

44. Find x so that l || m (7x–1) o l m

46. 3.6 Perpendiculars and Distance

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

48. Draw the segment that represents the distance from P to AB. P BA P BA

49. P BA P BA

50. P B A P B A