Name _____________________ 1.0 Homework Sketch each of the following. 1. AB
2. BA
3. BA
Use the figure at the right for #4-6. 4. Name all the labeled segments. R
5. Name all the labeled rays.
S T
6a. Name a pair of opposite rays with T as an endpoint.
W
b. Name another pair of opposite rays in the figure.
7. Name the angle in four ways.
C 1 P
M
Are the points collinear? If so, name the line on which they lie. 8. A, D, E
m A
9. B, C, F
G D
10. F, B, D
C
B
F
E 11. G, F, C
12. Name line m in three other ways. a. b. c.
Use with #8-12
n
Name the plane represented by each surface of the box. 13. the bottom G
E F
14. the front
H C
D A
15 the left side
B
X
Name the intersection of each pair of planes. 16. planes QRS and RSW
W
U
V
17. planes XWV and UVR T Name two planes that intersect in the given line 18. QU 19. XT
Q
U
T Q
U
V
S
R
22. T, V, R
X
W
Name another point in each plane. 23. plane UVW
X
W
W
U
V
T Q
R Use for #16-19
Shade the plane that contains the given points. 20. R, V, W 21. U, X, S X
S
T
S
R
V
S
Q
R
X 24. plane TUX
U
Is the given point coplanar with the other three points? 25. point Q with V, W, S 26. point W with X, V, R
W V
T Q
S R
Use for #23-26
Name the intersection between the following: 27. XT and QT
X
28 point S and plane WVR
W
U
V
29. UV and plane XTR 30. plane XTQ and plane UWS
T
S
31. RX and plane WST Q 32. TR and plane SRQ
R Use for #27-32
Find the plane containing the first three points listed. Decide whether the fourth point is in that plane. Write coplanar or noncoplanar to describe the points. 33. S, U, V, Y Z Y
34. X, S, V, U
S
U
V X
35. S, V, C, Y
C
If possible, draw a figure to fit each description. Otherwise, write not possible. 36. Four points that are collinear.
37. Two points that are noncollinear.
38. Three points that are noncollinear.
39. Three points that are noncoplanar.
Graph the points and state whether they are collinear. 40. (3, –3), (2, – 3), (–3, 1)
Use always, sometimes, or never to make a true statement. 41. Intersecting lines are _______________ coplanar. 42. Two planes ________________ intersect in exactly one point. 43. Three points are ________________ coplanar. 44. A plane containing two points of a line ________________ contains the entire line. 45. Four points are __________________ coplanar. 46. Two lines ___________________ meet in more than one point. Are the figures the same? Explain. 47. XY and YX __________________________________________________________________ __________________________________________________________________ 48. XY and YX __________________________________________________________________ __________________________________________________________________ 49. XY and YX __________________________________________________________________ __________________________________________________________________
Write out the postulate that explains each situation. 50. A land surveyor can always find a straight line from the point where she stands to any other point she can see.
51. A carpenter knows that a line can represent the intersection of two flat walls.
52. A furniture maker knows that a three-legged table is always steady, but a fourlegged table will sometimes wobble.
53. Navigation Rescue teams need to determine the location of a distress signal. In the diagram, the ship at point A receives a signal from the northeast. A ship at point B receives the same signal from due west. Trace the diagram and find the location of the distress signal. Explain how postulates help located the distress signal. ___________________________________________________________Source: Prentice Hall Geometry ________________________________________________________________ 54. How many planes contain the same three collinear points? Explain. ________________________________________________________________ ________________________________________________________________
Answers 1.
2.
3. 4. RS , RT , RW , ST , SW , TW 5. RS , ST , TW , WT , TS , SR 6. a. TS or TR and TW b. SR , ST 7.
1,
C,
PCM ,
MCP
8. no 9. yes, line n 10. yes, line n 11. no 12. Answers may vary. Sample: AE , EC , GA 13. plane ABCD 14. plane ABHF 15. plane EFAD 16. RS 17. UV 18. plane QUX and plane QUV 19. plane UXT and plane WXT 20.
21.
22.
23. X 24. Q 25. No 26. No 27. point T 28. point S 29. point V 30. UQ 31. point X 32. TR 33. coplanar 34. coplanar 35. noncoplanar 36. 37. not possible 38. 39. not possible 40.
41. always 42. never 43. always 44. always 45. sometimes 46. never 47. Yes; both name the segment with endpoints X and Y 48. No; the two rays have different endpoints. 49. Yes; both are the line through points X and Y. 50. Through any two points there is exactly one line. 51. If two planes intersect, then they intersect in exactly one line. 52. Through any three noncollinear points, there is exactly one plane. 53. Through any two points there is exactly one line so points A and D determine a line and points B and D determine a line. The distress signal is on both lines then point D is the distress signal because if two lines intersect, then they intersect in exactly one point. 54. Infinitely many. If three points are on one line, then infinitely many planes can contain that one line.
