B Apply

How many pairs of each type of angles do two lines and a transversal form?

25. alternate interior angles
26. corresponding angles
27. alternate exterior angles
28. vertical angles
29. Recreation You and a friend are driving go-karts on two different tracks. As you drive on a straight section heading east, your friend passes above you on a straight section heading south. Are these sections of the two tracks parallel, skew, or neither? Explain.

In Exercises 30–35, describe the statement as true or false. If false, explain. Assume that lines and planes that appear to be parallel are parallel.

30. C B ↔ || H G ↔ modified c b with left right arrow above , vertical linevertical line , modified h g with left right arrow above
31. E D ↔ || H G ↔ modified e d with left right arrow above , vertical linevertical line , modified h g with left right arrow above
32. plane  AED ||  plane  FGH plane
33. plane  ABH ||  plane  CDF plane
34. A B ↔ modified eh b with left right arrow above  and H G ↔ modified h g with left right arrow above  are skew lines.
35. A E ↔ modified eh e with left right arrow above  and B C ↔ modified b c with left right arrow above  are skew lines.
36. Think About a Plan A rectangular rug covers the floor in a living room. One of the walls in the same living room is painted blue. Are the rug and the blue wall parallel? Explain.
    • Can you visualize the rug and the wall as geometric figures?
    • What must be true for these geometric figures to be parallel?

In Exercises 37–42, determine whether each statement is always, sometimes, or never true.

37. Two parallel lines are coplanar.
38. Two skew lines are coplanar.
39. Two planes that do not intersect are parallel.
40. Two lines that lie in parallel planes are parallel.
41. Two lines in intersecting planes are skew.
42. A line and a plane that do not intersect are skew.
43. 1. Writing Describe the three ways in which two lines may be related.
    2. Give examples from the real world to illustrate each of the relationships you described in part (a).
44. Open-Ended The letter Z illustrates alternate interior angles. Find at least two other letters that illustrate pairs of angles presented in this lesson. Draw the letters. Then mark and describe the angles.
45. 1. Reasoning Suppose two parallel planes A and B are each intersected by a third plane C. Make a conjecture about the intersection of planes A and C and the intersection of planes B and C.
    2. Find examples in your classroom to illustrate your conjecture in part (a).

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