B Apply

Postulate 1-4 states that any three noncollinear points lie in exactly one plane. Find the plane that contains the first three points listed. Then determine whether the fourth point is in that plane. Write coplanar or noncoplanar to describe the points.

27. Z, S, Y, C
28. S, U, V, Y
29. X, Y, Z, U
30. X, S, V, U
31. X, Z, S, V
32. S, V, C, Y

If possible, draw a figure to fit each description. Otherwise, write not possible.

33. four points that are collinear
34. two points that are noncollinear
35. three points that are noncollinear
36. three points that are noncoplanar
37. Open-Ended Draw a figure with points B, C, D, E, F, and G that shows C D ↔ , B G ↔ , modified c d with left right arrow above , comma , modified b g with left right arrow above , comma  and E F ↔ , modified e f with left right arrow above , comma  with one of the points on all three lines.

38. Think About a Plan Your friend drew the diagram below to prove to you that two planes can intersect in exactly one point. Describe your friend's error.

    

    • How do you describe a plane?
    • What does it mean for two planes to intersect each other?
    • Can you define an endpoint of a plane?
39. Reasoning If one ray contains another ray, are they the same ray? Explain.

For Exercises 40–45, determine whether each statement is always, sometimes, or never true.

40. T Q ↔ modified t q with left right arrow above  and Q T ↔ modified q t with left right arrow above  are the same line.
41. J K → j k vector  and J L → j l vector  are the same ray.
42. Intersecting lines are coplanar.
43. Four points are coplanar.
44. A plane containing two points of a line contains the entire line.
45. Two distinct lines intersect in more than one point.

46. Use the diagram below. How many planes contain each line and point?

    
    Image Long Description

    1. E F ↔ modified e f with left right arrow above  and point G
    2. P H ↔ modified p h with left right arrow above  and point E
    3. F G ↔ modified f g with left right arrow above  and point P
    4. E P ↔ modified e p with left right arrow above  and point G

    5. Reasoning What do you think is true of a line and a point not on the line? Explain. (Hint: Use two of the postulates you learned in this lesson.)

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