1. GOALS of High School GEOMETRY
MEASUREMENT
Remember the Grade School Rules of how
to MEASURE and add to/connect them
EXTENSION
Learn the METHODS & LOGIC of Extending
the Measurement Rules to New Ideas
ABSTRACTION
Learn how to change geometric measurement
problems to algebra problems and vice versa

2. GOALS of High School GEOMETRY
ABSTRACTION
A group of seven weary men once arrived at a small
hotel and asked for accommodations for the night,
specifying that they wanted separate rooms.  The
manager admitted that he had only six rooms left,
but thought he might be able to put up his guests
as they desired. 
He took the first man to the first room and asked one
of the other men to stay there for a few minutes.  He
then took the third man to the second room, the fourth
man to the third room, the fifth man to the fourth room
and the sixth man to the fifth room.  Then he returned to
the first room, got the seventh man, and showed him to
the sixth room. 
Everyone was thus nicely taken care of.  Or was he?

3. Splash Screen

4. Identify and model points, lines, and planes.
Identify collinear and coplanar points and intersecting lines and planes in space.
undefined term
plane
coplanar
space
locus
intersection
point
line
collinear
Lesson 1 MI/Vocab

5. Undefined Terms – Words, usually readily understood,
that are NOT formally explained by means of more
basic words and concepts. The basic undefined terms
of Geometry are point, line and plane.
POINT – a location in space with NO LENGTH or WIDTH.
LINE – an infinite set of points with INFINITE LENGTH,
but NO WIDTH.
PLANE – an infinite SET of points with INFINITE
LENGTH, INFINITE WIDTH, but NO THICKNESS. 22

6. SPACE – The boundless 3-dimensional set of
of ALL POINTS.
COLLINEAR – Points that lie on the SAME LINE.
COPLANAR – Points that line in the SAME PLANE.
LOCUS – The set of points that SATISFY a GIVEN
CONDITION.
INTERSECTION - the SET of POINTS
that are CONTAINED in BOTH Figures

7. Lesson 1 KC1

8. Lesson 1 KC1

9. Lesson 1 KC1

10. Lesson 1 KC1

11. Lesson 1 KC1

12. A. Use the figure to name a line containing point K.
Name Lines and Planes
A. Use the figure to name a line containing point K.
Answer: The line can be named as line a.
There are three points on the line. Any two of the points can be used to name the line.
Lesson 1 Ex1

13. B. Use the figure to name a plane containing point L.
Name Lines and Planes
B. Use the figure to name a plane containing point L.
Answer: The plane can be named as plane B.
You can also use the letters of any three noncollinear points to name the plane.
plane JKM plane KLM plane JLM
Lesson 1 Ex1

14. Name Lines and Planes
The letters of each of these names can be reordered to create other acceptable names for this plane. For example, JKM can also be written as JMK, MKJ, KJM, KMJ, and MJK. There are 15 different three-letter names for this plane.
Lesson 1 Ex1

15. A. Use the figure to name a line containing the point X.
A. line X
B. line c
C. line Z D. A B C D
Lesson 1 CYP1

16. B. Use the figure to name a plane containing point Z.
A. plane XY
B. plane c
C. plane XQY
D. plane P A B C D
Lesson 1 CYP1

17. Model Points, Lines, and Planes
A. Name the geometric shape modeled by a 10  12 patio.
Answer: The patio models a plane.
Lesson 1 Ex2

18. Model Points, Lines, and Planes
B. Name the geometric shape modeled by a drop of water on a table.
Answer: The drop on the table models a point on a plane.
Lesson 1 Ex2

19. A. VISUALIZATION Name the geometric shape modeled by a colored dot on a map used to mark the location of a city.
A. point
B. line segment
C. plane
D. none of the above A B C D
Lesson 1 CYP2

20. B. VISUALIZATION Name the geometric shape modeled by the ceiling of your classroom.
A. point
B. line segment
C. plane
D. none of the above A B C D
Lesson 1 CYP2

21. Draw Geometric Figures
Draw a surface to represent plane R and label it.
Lesson 1 Ex3

22. Draw Geometric Figures
Draw a line anywhere on the plane.
Lesson 1 Ex3

23. Draw Geometric Figures
Draw dots on the line for point A and B. Label the points.
Lesson 1 Ex3

24. Draw Geometric Figures
Lesson 1 Ex3

25. Draw Geometric Figures
Draw dots on this line for point D and E. Label the points.
Lesson 1 Ex3

26. Draw Geometric Figures
Label the intersection point of the two lines as P.
Lesson 1 Ex3

27. Draw Geometric Figures
Answer:
Lesson 1 Ex3

28. Draw Geometric Figures
Answer:
There are an infinite number of points that are collinear with Q and R. In the graph, one such point is T(1, 0).
Lesson 1 Ex3

29. A. Choose the best diagram for the given relationship
A. Choose the best diagram for the given relationship. Plane D contains line a, line m, and line t, with all three lines intersecting at point Z. Also point F is on plane D and is not collinear with any of the three given lines.
A. B.
C. D. A B C D
Lesson 1 CYP3

30. Lesson 1 CYP3

31. A. B.
C. D. A B C D
Lesson 1 CYP3

32. A. How many planes appear in this figure?
Interpret Drawings
A. How many planes appear in this figure?
Answer: There are two planes: plane S and plane ABC.
Lesson 1 Ex4

33. B. Name three points that are collinear.
Interpret Drawings
B. Name three points that are collinear.
Answer: Points A, B, and D are collinear.
Lesson 1 Ex4

34. C. Are points A, B, C, and D coplanar? Explain.
Interpret Drawings
C. Are points A, B, C, and D coplanar? Explain.
Answer: Points A, B, C, and D all lie in plane ABC, so they are coplanar.
Lesson 1 Ex4

35. Answer: The two lines intersect at point A.
Interpret Drawings
Answer: The two lines intersect at point A.
Lesson 1 Ex4

36. Intersecting Terms
Intersection Possibilities
Point
Line
Plane

37. A. How many planes appear in this figure?
A. one
B. two
C. three
D. four A B C D
Lesson 1 CYP4

38. B. Name three points that are collinear.
A. B, O, and X
B. X, O, and N
C. R, O, and B
D. A, X, and Z A B C D
Lesson 1 CYP4

39. C. Are point X, O, and R coplanar?
A. yes
B. no
C. cannot be determined A B C
Lesson 1 CYP4

40. A. point X
B. point N
C. point R
D. point A A B C D
Lesson 1 CYP4

41. DEFINE the BIG Three Undefined Terms
You should be able to:
DEFINE the BIG Three Undefined Terms
DESCRIBE the Attributes of each Undefined Term
DESCRIBE the resulting INTERSECTION of
Undefined Terms as a point, line or plane
DETERMINE how many COLLINEAR points are
needed to define a Line and a Plane
Lesson 1 CYP4

43. Five-Minute Checks Image Bank Math Tools Animation Menu
Archeology and the Coordinate Plane
CR Menu

44. Lesson 1-2 (over Lesson 1-1) Lesson 1-3 (over Lesson 1-2)
5Min Menu

45. 1. Exit this presentation.
To use the images that are on the following three slides in your own presentation:
1. Exit this presentation.
2. Open a chapter presentation using a full installation of Microsoft® PowerPoint® in editing mode and scroll to the Image Bank slides.
3. Select an image, copy it, and paste it into your presentation.
IB 1

46. IB 2

47. IB 3

48. IB 4

49. 1-4-1 Using a Protractor to Measure Three Types of Angles
Copy an Angle
1-4-3 Bisect an Angle
1-5 Constructing Perpendiculars
1-7 Orthographic Drawings
Animation Menu

50. Animation 1

51. Animation 2

52. Animation 3

53. Animation 4

54. Animation 5

55. What is the value of x2 + 3yz if x = 3, y = 6, and z = 4?
B. 75
C. 78
D. 81 A B C D
5Min 1-1

56. Solve 2(x – 7) = 5x + 4. A.
B. –6 C.
D. 6 A B C D
5Min 1-2

57. Is (–2, 5) a solution of 3x + 4y = 14?
A. yes
B. no A B
5Min 1-3

58. Factor 9x2 – 25y2. A. (3x + 5y)2 B. 3x2 + 5y2 C. (3x – 5y)2
D. (3x + 5y)(3x – 5y) A B C D
5Min 1-4

59. Which choice shows the graph of y = 3x + 2?
A B.
C D. A B C D
5Min 1-5

60. Find all of the solutions of 2x2 + 5x – 3 = 0.
A. –3 only B. C.
D. no solution A B C D
5Min 1-6

61. Refer to the figure. Name three collinear points.
(over Lesson 1-1)
Refer to the figure. Name three collinear points.
A. Q, T, B
B. Q, T, A
C. L, T, B
D. A, T, B A B C D
5Min 2-1

62. Refer to the figure. What is another name for line AB?
(over Lesson 1-1)
Refer to the figure. What is another name for line AB? A.
B. line ℓ, C. D. A B C D
5Min 2-2

63. Refer to the figure. Name a line in plane Z.
(over Lesson 1-1)
Refer to the figure. Name a line in plane Z. A.
B. line ℓ or C. D. A B C D
5Min 2-3

64. Refer to the figure. Name the intersection of planes Z and W.
(over Lesson 1-1)
Refer to the figure. Name the intersection of planes Z and W. A. B. C.
D. line ℓ A B C D
5Min 2-4

65. Refer to the figure. How many lines are in plane Z?
(over Lesson 1-1)
Refer to the figure. How many lines are in plane Z?
A. zero
B. two
C. four
D. infinitely many A B C D
5Min 2-5

66. (over Lesson 1-1)
Three lines are coplanar. What is the greatest number of intersection points that can exist?
A. 2
B. 3
C. 4
D. 5 A B C D
5Min 2-6

67. Find the precision for a measurement of 42 centimeters.
(over Lesson 1-2)
Find the precision for a measurement of 42 centimeters.
A cm to cm
B. 41 cm to 43 cm
C cm to 42.5 cm
D cm to cm A B C D
5Min 3-1

68. (over Lesson 1-2)
If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1, find x and MN.
A. x = 2, MN = 5
B. x = 2, MN = 1
C. x = 5, MN =4
D. x = 1.5, MN = 0.5 A B C D
5Min 3-2

69. Use the figure to find RT.
(over Lesson 1-2)
Use the figure to find RT. A. B. C. D. A B C D
5Min 3-3

70. A B Use the figure to determine whether MN is congruent to QM. A. yes
(over Lesson 1-2)
Use the figure to determine whether MN is congruent to QM.
A. yes
B. no A B
5Min 3-4

71. A B Use the figure to determine whether MQ is congruent to NQ. A. yes
(over Lesson 1-2)
Use the figure to determine whether MQ is congruent to NQ.
A. yes
B. no A B
5Min 3-5

72. If AB is congruent to BC, AB = 4x – 2, and BC = 3x + 3, find x.
(over Lesson 1-2)
If AB is congruent to BC, AB = 4x – 2, and BC = 3x + 3, find x.
A. 5
B. 4
C. 3
D. 2 A B C D
5Min 3-6

73. Use the number line to find the measure of AC.
(over Lesson 1-3)
Use the number line to find the measure of AC.
A. 2
B. 3
C. 4
D. 5 A B C D
5Min 4-1

74. Use the number line to find the measure of DE.
(over Lesson 1-3)
Use the number line to find the measure of DE.
A. 9
B. 8.5
C. 8
D. 7 A B C D
5Min 4-2

75. Use the number line to find the midpoint of EG.
(over Lesson 1-3)
Use the number line to find the midpoint of EG.
A. E
B. F
C. G
D. H A B C D
5Min 4-3

76. Find the distance between P(–2, 5) and Q(4, –3).
(over Lesson 1-3)
Find the distance between P(–2, 5) and Q(4, –3).
A. 10
B. 8.12
C. 9
D. 6.32 A B C D
5Min 4-4

77. (over Lesson 1-3)
Find the coordinates of R if M(–4, 5) is the midpoint of RS and S has coordinates (0, –10).
A. (8, 20)
B. (8, –20)
C. (–8, 20)
D. (–8, 0) A B C D
5Min 4-5

78. (over Lesson 1-3)
What is the perimeter of triangle DEF if its vertices are D(–2, –6), E(–2, 6) and F(3, –6)?
A. 12 units
B. 13 units
C. 17 units
D. 30 units A B C D
5Min 4-6

79. Refer to the figure. Name the vertex of 3.
(over Lesson 1-4)
Refer to the figure. Name the vertex of 3.
A. A
B. B
C. C
D. D A B C D
5Min 5-1

80. Refer to the figure. Name a point in the interior of ACB.
(over Lesson 1-4)
Refer to the figure. Name a point in the interior of ACB.
A. G
B. D
C. B
D. A A B C D
5Min 5-2

81. Refer to the figure. Name the sides of BAC.
(over Lesson 1-4)
Refer to the figure. Name the sides of BAC. A. B. C. D. A B C D
5Min 5-3

82. (over Lesson 1-4)
Refer to the figure. Name the angles with vertex B that appear to be acute.
A. BAC, BDC, BDA
B. BDC, BCA, BAC
C. CAB, CDB, DCB
D. ABC, ABD, DBC A B C D
5Min 5-4

83. (over Lesson 1-4)
Refer to the figure. If bisects ABC, mABD = 2x + 3, and mDBC = 3x – 13, find mABD.
A. 70
B. 35
C. 32
D. 16 A B C D
5Min 5-5

84. (over Lesson 1-4)
If P is in the interior of MON and mMOP = mMON, what can you conclude?
A. PON  NOM
B. MON is an acute angle. C.
D. mMOP > mPON A B C D
5Min 5-6

85. Refer to the figure. Name two acute vertical angles.
(over Lesson 1-5)
Refer to the figure. Name two acute vertical angles.
A. AEB and AED
B. AED and BEC
C. DEC and CEB
D. AEB and DEC A B C D
5Min 6-1

86. Refer to the figure. Name a linear pair whose vertex is E.
(over Lesson 1-5)
Refer to the figure. Name a linear pair whose vertex is E.
A. AEB, DEC
B. AEB, AED
C. AED, BEC
D. CED, BEA A B C D
5Min 6-2

87. Refer to the figure. Name an angle supplementary to BEC.
(over Lesson 1-5)
Refer to the figure. Name an angle supplementary to BEC.
A. CED
B. DEA
C. AED
D. AEC A B C D
5Min 6-3

88. (over Lesson 1-5)
1 and 2 are a pair of supplementary angles, and the measure of 1 is twice the measure of 2. Find the measures of both angles.
A. m1 = 60, m2 = 120
B. m1 = 30, m2 = 60
C. m1 = 120, m2 = 60
D. m1 = 60, m2 = 30 A B C D
5Min 6-4

89. (over Lesson 1-5)
If RS is perpendicular to ST and is the angle bisector of RST, what is mTSV?
A. 180
B. 90
C. 60
D. 45 A B C D
5Min 6-5

90. If two angles are both congruent and supplementary, they must be ? .
(over Lesson 1-5)
If two angles are both congruent and supplementary, they must be ? .
A. two right angles
B. two acute angles
C. two obtuse angles
D. an obtuse and an acute angle A B C D
5Min 6-6

91. Name polygon A by its number of sides.
(over Lesson 1-6)
Name polygon A by its number of sides.
A. pentagon
B. nonagon
C. heptagon
D. octagon A B C D
5Min 7-1

92. Name polygon B by its number of sides.
(over Lesson 1-6)
Name polygon B by its number of sides.
A. pentagon
B. nonagon
C. heptagon
D. octagon A B C D
5Min 7-2

93. Find the perimeter of polygon A.
(over Lesson 1-6)
Find the perimeter of polygon A.
A. 35 cm
B. 40 cm
C. 25 cm
D. 30 cm A B C D
5Min 7-3

94. Find the perimeter of polygon B.
(over Lesson 1-6)
Find the perimeter of polygon B.
A. 40 in.
B. 45 in.
C. 42 in.
D. 43 in. A B C D
5Min 7-4

95. Classify the polygons as regular or irregular.
(over Lesson 1-6)
Classify the polygons as regular or irregular.
A. polygon A: regular; polygon B: regular
B. polygon A: regular; polygon B: irregular
C. polygon A: irregular; polygon B: regular
D. polygon A: irregular; polygon B: irregular A B C D
5Min 7-5

96. (over Lesson 1-6)
What is the area of rectangle FGHJ if its vertices are F(–3, 2), G(4, 2), H(4, –3), and J(–3, –3)?
A. 24 square units
B. 35 square units
C. 49 square units
D. 25 square units A B C D
5Min 7-6

97. This slide is intentionally blank.
End of Custom Shows