62
Geometry CC RHS Unit 1 Points, Planes, & Lines 1 GEOMETRY Unit 1 Points, Planes, & Lines Prepared by: G. Alvarez-Garcia, S. George, & R. Mercadante
Geometry CC RHS Unit 1 Points, Planes, & Lines 1
GEOMETRY Unit 1
Points, Planes, & Lines
Prepared by:
G. Alvarez-Garcia, S. George, & R. Mercadante
Geometry CC RHS Unit 1 Points, Planes, & Lines 2
1.1 Points, Lines, and Planes
Definition
The “easy”
definition
What does it
look like?
How is it
written?
A point has no ________________.
A line extends in _______
dimension.
A plane extends in _______
dimensions.
A line segment AB consists of
____________ A and B, and all the
points on line AB that are
________________ A and B.
A ray AB consists of the initial point
____ and all the points on the line AB
that lie on _____________
__________ of A as point B.
THINK ABOUT IT! Is there a difference between lines ̅̅ ̅̅ and ̅̅ ̅̅ ?
Is there difference between ⃗⃗⃗⃗ ⃗ and ⃗⃗⃗⃗ ⃗?
Example 1: Give all the names of the figures shown below. 1. 2. 3. 4.
5.
6.
E
FC D
E
F
GI
J
J
OP
PR
E
F
GI
J
OP
QM
N
J
OP
O
Geometry CC RHS Unit 1 Points, Planes, & Lines 3
Example 2: Name segments and rays. a. Give another name for ̅̅ ̅̅ .
b. True or false: ⃡⃗ ⃗ and ⃡⃗⃗⃗ ⃗ are the same line.
c. ⃗⃗⃗⃗ ⃗ and ____ are the same rays.
d. Name all the points given on ⃡⃗⃗⃗ ⃗. Postulate
Theorem U is between L and V
The Name vs. Its Measure
SEGMENT ADDITION POSTULATE
Example 1: Draw a diagram and write the word form. 1. I is between J and M. 2. T is between A and E.
● J
When points
are created
by
intersection
s of lines,
• J H ●
If B is between A and C,
then
_______________________.
LIL + LIL =
BIG
A B 6 in
_____+______=______
Geometry CC RHS Unit 1 Points, Planes, & Lines 4
Example 2: Using Segment Addition Postulate
1. a) O is between M and P. Find the length of ̅̅̅̅̅
if and PO = 14.
b) What would your reasoning be if asked to
explain why you set up the equation above?
2. E is be between N and T. If and
, find the length of ̅̅̅̅ and explain.
3. Y is be between X and Z. If and
find the length of ̅̅̅̅ and explain.
4. A is be between H and T. If ,
, and , solve for . Explain.
5. I is be between K and D. If ,
, and , find . Explain. 6. G is be between P and A. If ,
, and , solve for . Explain.
N
T
E
H TA
Geometry CC RHS Unit 1 Points, Planes, & Lines 5
Regents Test
Basic Concepts and Definitions
Questions 1 through 9 refer to the following:
1) PR and TS determine a plane. TRUE FALSE
2) Points T, Q, and S are collinear. TRUE FALSE
3) S is between P and R. TRUE FALSE
4) Points P, Q, and R are collinear. TRUE FALSE
5) PR and TS intersect at Q. TRUE FALSE
6) Points T, Q, and S are non-collinear. TRUE FALSE
7) Points P, Q, and T are non-collinear. TRUE FALSE
8) Q is between P and R. TRUE FALSE
9) Points S, Q, and R are collinear. TRUE FALSE
Questions 10 through 16 refer to the following:
In the diagram below, points P, N, and Q are collinear. Indicate whether the given statement is True or False.
10) Points M, N, K and Q are coplanar. TRUE FALSE
11) Points P, K, and Q determine a plane. TRUE FALSE
12) Only one plane contains points P, N, and Q. TRUE FALSE
13) PQ and NK intersect at N. TRUE FALSE
Geometry CC RHS Unit 1 Points, Planes, & Lines 6
14) Points N, K, and M determine a plane. TRUE FALSE
15) KN and M determine a plane. TRUE FALSE
Geometry CC RHS Unit 1 Points, Planes, & Lines 7
16) Points P, K, N, and Q are coplanar. TRUE FALSE
17) If two planes intersect, then their intersection is a line. TRUE FALSE
18) PQ has no endpoints. TRUE FALSE
19) PQ has only one endpoint. TRUE FALSE
20) A line segment has exactly one midpoint. TRUE FALSE
21) Tell whether a point, a line, or a plane is illustrated by .
22) Tell whether a point, a line, or a plane is illustrated by .
23) PQ has no endpoints. TRUE FALSE
24) FG has only one endpoint. TRUE FALSE
25) PQ has two endpoints. TRUE FALSE
26) Tell whether a point, a line, or a plane is illustrated by the top of a desk.
1900 - 1 - Page 2
Geometry CC RHS Unit 1 Points, Planes, & Lines 8
27) If two lines intersect, then their intersection is a point. TRUE FALSE
28) It is possible to define each geometric term by using previously defined geometric terms. TRUE FALSE
29) AB has no endpoints. TRUE FALSE
30) Another name for PQ is QP. TRUE FALSE
31) Tell whether a point, a line, or a plane is illustrated by the tip of a pen.
32) Tell whether a point, a line, or a plane is illustrated by the edge of a textbook.
33) CD has two endpoints. TRUE FALSE
34) Tell whether a point, a line or a plane is illustrated by a basketball backboard.
35) Another name for PQ is QP. TRUE FALSE
36) PQ has two endpoints. TRUE FALSE
Geometry CC RHS Unit 1 Points, Planes, & Lines 9
Regents Test Points, Planes, & Lines: Concepts of a POSTULATE and THEOREM
1) A theorem is a statement that can be proven. TRUE FALSE
Questions 2 through 6 refer to the following:
Write the given statement in If..., then... form.
2) Perpendicular lines form four right angles.
3) Vertical angles are congruent.
4) Two triangles have the same area if they are congruent.
5) Every rational number is real.
6) A person living in Maryland lives in the United States.
Questions 7 through 12 refer to the following:
State the hypothesis and conclusion of the given statement.
7) Two intersecting lines form vertical angles.
8) If y - 3 = 7, then y = 10.
9) You will score a run if you hit a home run.
10) If the sum of the measure of two angles is 180D, then the angles are supplementary.
11) If two angles are right angles, then they are congruent.
12) If two sides of a triangle are congruent, then the triangle is isosceles.
Geometry CC RHS Unit 1 Points, Planes, & Lines 10
13) Define a postulate.
14) A theorem is a statement accepted without proof. TRUE FALSE
15) A postulate is a statement that must be proven. TRUE FALSE
16) A postulate can be used in the proof of a theorem. TRUE FALSE
17) A postulate can not be used in the proof of a theorem. TRUE FALSE
18) A postulate is a true statement accepted without proof. TRUE FALSE
19) Explain the difference between a postulate and a theorem.
20) All statements in Geometry are definitions or postulates. TRUE FALSE
Geometry CC RHS Unit 1 Points, Planes, & Lines 11
Regents Test
Points, Planes, & Lines: Concepts involving
Definitions Questions 1 through 5 refer to the following:
Arrange the following terms in the order in which their definitions should be stated.
1) ray, angle, endpoint of a ray
2) isosceles triangle, triangle, base of an isosceles triangle
3) congruent angles, angle bisector, angle
4) angle, acute triangle, acute angle
5) midpoint of a segment, segment, congruent segments
6) Point is a defined term. TRUE FALSE
7) Point is an undefined term. TRUE FALSE
Questions 8 through 11 refer to the following:
Explain why the following is not a good definition.
8) A line segment is a geometric figure.
9) Coplanar points are points in the same plane.
10) An isosceles triangle is when a triangle has two sides the same length.
11) A square is something not round.
12) Plane is a defined term. TRUE FALSE
13) Line is a defined term. TRUE FALSE
14) Define AB written out with words.
Geometry CC RHS Unit 1 Points, Planes, & Lines 12
15) Define AB written out with words.
16) Plane is an undefined term. TRUE FALSE
17) Define AB written out with words.
18) Ray is not an undefined term. TRUE FALSE
19) Line is an undefined term. TRUE FALSE
20) Define AB written out with words.
Geometry CC RHS Unit 1 Points, Planes, & Lines 13
1.2 Congruent Segments
Congruent
vs. ̅̅ ̅̅
Amy’sHeight = Tim’s Height Amy ____ Tim
Segments Lengths are
Equal
Segments are
Congruent
MARKING UP CONGRUENT SEGMENTS
1. Mark the following segments congruent: ̅̅̅̅ ̅, ̅̅ ̅̅ ̅̅ ̅̅ , and ̅̅ ̅ ̅
2. Then IJ = ____, ML = _____, and HM = _____
Midpoint: (Equal parts)
How to say it: ____ is the midpoint of
_____
Bisect: (Cuts the second one in half)
How to say it: _____ bisects _____ at point ___
Example 1: Draw a diagram and write the word form. 1. O is the midpoint of ̅̅ ̅̅ 2. ̅̅ ̅̅ ̅ bisects ̅̅ ̅̅ at O. 3. A is between F and T.
4. ̅̅ ̅̅ ̅ bisects ̅̅ ̅̅ at U. 5. U is between B and M. 6. E is the midpoint of ̅̅ ̅̅
LIL = LIL LIL = LIL
A B
C D
5’4”
Amy Tim
M SDK DP
G
Geometry CC RHS Unit 1 Points, Planes, & Lines 14
Example 2: Finding segment lengths 1. is the midpoint of ̅̅ ̅̅ , If AG =13, find TA. Explain.
2. ̅̅ ̅̅ bisects ̅̅ ̅̅ at . If , find .
Explain.
3. ̅̅̅̅ bisects ̅̅ ̅̅ at . If and ,
find and . Explain.
4. is the midpoint of ̅̅̅̅ , If PT=26, find PF. Explain.
3. Point S is the midpoint of ̅̅ ̅̅ . If
and , solve for and explain.
4. A is between J and M. If ,
, and . Solve for and
explain.
EF
M N
JO
P
O
T GA
T
B
A
D
R
R
TS
Geometry CC RHS Unit 1 Points, Planes, & Lines 15
5. M is between N and L. If ,
, and , find NM and
explain.
6. Let ̅̅ ̅̅ bisect ̅̅̅̅ at point O, where
and – , find JO and explain.
ooh! I <3 PROOFS!
Given: is the midpoint of ̅̅ ̅̅
;
Prove:
Statements Reasons
1. is the midpoint of ̅̅ ̅̅
;
2.
3.
4.
5.
6.
1.
2.
3.
4.
5.
6.
Geometry CC RHS Unit 1 Points, Planes, & Lines 16
Regents Test Points, Planes, & Lines: Lines and Line Segments
Questions 1 through 17 refer to the following:
Use the figure below to name a segment, ray, or point that
best completes the given statement.
1) the length of NK is G
2) G is the midpoint of MT
3) NK = NO + G
4) EA = ER - G
5) TW = TK - G
6) EA + AR = OK + G
7) WK C G
8) the ray opposite TK is G
9) G is the midpoint of NK
Geometry CC RHS Unit 1 Points, Planes, & Lines 17
10) T is the midpoint of G
11) ER C G
12) AR = AW + G
13) the length of MW is G
14) the ray opposite AM is G
15) another name for ET is G
16) R is the midpoint of G
17) another name for AR is G
18) Find PR, given that Q is the midpoint of PR and QR
= 8.
19) Find PQ, given that Q is the midpoint of PR and PR
= 20.
20) Find the value of x if B is the midpoint of AC, AB
= x - 3, and AC = 6x - 38.
Geometry CC RHS Unit 1 Points, Planes, & Lines 18
21) Find the value of x if B is the midpoint of AC,
AB = 2x + 9, and AC = 34.
22) Find PR, given that Q is the midpoint of PR and
PQ = 5.
23) Find QR, given that Q is the midpoint of PR and
PQ = 5.
24) Find the value of x if B is the midpoint of AC,
AB = 4x - 1, and AC = 46.
25) Find PQ, given that Q is the midpoint of PR and
PR = 11.
26) Find the value of x if B is the midpoint of AC, AB = 3x
- 3, and BC = 21.
27) Find the value of x if B is the midpoint of AC,
AB = 3x + 1, and AC = 10x - 22.
28) Find the value of x if B is the midpoint of AC,
AB = 10 - x, and BC = 2x + 37.
29) Find PQ, in terms of x, given that Q is the midpoint
of PR and PR = 2x + 4.
30) Find the value of x if B is the midpoint of AC,
AB = 5x + 4, and BC = 2x + 37.
Geometry CC RHS Unit 1 Points, Planes, & Lines 19
Regents Test
Points, Planes, & Lines: Separation of Points and Collinear Points
Questions 1 through 8 refer to the following:
Find the value of x if A, B, and C are collinear points and
B is between A and C.
1) AB = 6x, BC = x - 5, AC = 23
2) AB = 5, BC = 3x + 7, AC = 5x - 2
3) AB = 12, BC = 5x - 2, AC = 3x + 20
4) AB = x, BC = x + 2, AC = 14
5) AB = x + 6, BC = 3x - 5, AC = 36 - x
6) AB = 2x, BC = x - 2, AC = 28
7) AB = 3x, BC = 2x - 7, AC = 2x + 35
8) AB = 5x - 1, BC = 14, AC = 25 - x
Questions 9 through 20 refer to the following:
9) Find the distance between S and F.
10) Find the distance between S and H.
Geometry CC RHS Unit 1 Points, Planes, & Lines 20
11) Find the distance between A and R.
12) Find the distance between E and M.
13) Find the distance between S and A.
14) Find the distance between S and R.
15) Find the distance between M and N.
16) Find the distance between R and A.
17) Find the distance between H and A.
18) Find the distance between N and F.
19) Find the distance between E and F.
20) Find the distance between E and N.
Questions 21 through 28 refer to the following:
Find the required distance if A, B and C are collinear
points and point B is between points A and C.
21) AB = 2, AC = 18, BC = G
Geometry CC RHS Unit 1 Points, Planes, & Lines 21
22) AC = 10, BC = 7, AB = G
23) AC = 19, BC = 8, AB = G
24) AB = 12, AC = 25, BC = G
25) AB = 4, BC = 9, AC = G
Geometry CC RHS Unit 1 Points, Planes, & Lines 22
26) BC = 11, AB = 5, AC = G
27) AB = 6, BC = 9, AC = G
28) BC = 20, AB = 7, AC = G
Geometry CC RHS Unit 1 Points, Planes, & Lines 23
Unit 1 Points, Lines & Planes
CLASSWORK & HOMEWORK
Points & Lines: CLASSWORK 1. Name three collinear points on line q and on line s
2. Name 4 sets of non-collinear points
3. Name the opposite rays on line q and on line s
4. How many points are marked on line q?
5. How many points are there on line q?
Points & Lines: HOMEWORK 6. Name three collinear points on line o
7. Name 4 sets of collinear points
8. Name two opposite rays on line j with endpoint R
9. Which 4 points are collinear? What line are they on?
10. How many points are there on line j?
Points & Lines: CLASSWORK Name a point that is collinear with the given points
11. O and S
12. P and R
13. U and T
14. U and S
15. Name 3 points non-collinear with T and V
Points & Lines: HOMEWORK 16. Q and S
Geometry CC RHS Unit 1 Points, Planes, & Lines 24
17. T and R
18. U and V
19. P and S
20. Name 3 points non-collinear with T and U
Planes: CLASSWORK
21. Name a point that is coplanar with A, E, and J
22. Name a point that is coplanar with A, C, and I
23. Name all the points that are noncoplanar with A, C, and D
24. Name all the points that are noncoplanar with F, H, and E
25. Where do plane ACH and plane IDC intersect?
26. Where do planes ACH, AFJ, and ACD intersect?
Planes: HOMEWORK 27. Name a point that is coplanar with E, D, and I
28. Name a point that is coplanar with A, E, and J
29. Name all the points that are noncoplanar with A, F, and H
30. Name all the points that are noncoplanar with A, F, and D
31. Where do plane JED and plane FHI intersect?
32. Where so planes AED, CHI, and JED intersect?
Congruence, Distance & Length: CLASSWORK
33. Find the distance between point K and point M
34. Find the distance between point P and point L
Geometry CC RHS Unit 1 Points, Planes, & Lines 25
35. Find the distance between point O and Point N
36. Find the distance between point L and point N
Congruence, Distance & Length: HOMEWORK 37. Find the distance between point N and point K
38. Find the distance between point Q and point L
39. Find the distance between point L and point P
40. Find the distance between point K and point Q
Geometry CC RHS Unit 1 Points, Planes, & Lines 26
Congruence, Distance & Length: CLASSWORK
Figure for #41-52
41. Find the distance between point G and point L
42. Find the distance between point K and point M
43. Find the distance between point A and Point D
44. Find the distance between point B and point F
45. Find the distance between point C and point H
46. Find the distance between point E and point N
Congruence, Distance & Length: HOMEWORK
47. Find the distance between point L and point A
48. Find the distance between point D and point L
49. Find the distance between point N and point K
50. Find the distance between point K and point H
51. Find the distance between point C and point I
Geometry CC RHS Unit 1 Points, Planes, & Lines 27
52. Find the distance between point B and point M
Congruence, Distance & Length: CLASSWORK
53. Given: RV = 24 SU = 8 RS = ST = TU
RS = ?
54. Given: RV = 24 SU = 8 RS = ST = TU
UV = ?
55. Given: RV = 37 RS = TU UV = 9 ST + UV = 15
ST = ? RS = ? SU = ?
56. Given: RV = 25 RT = 6 RS = ST = TU UV = 3x +1
x = ?
57. Points F, X, and D are collinear, with F between X and D. Draw a diagram and solve for X, if FX = 2x+13, FD = 7x-6, and XD = 2x+70.
58. P, A, and Z are collinear. Z is between P and A. Draw a diagram and solve for x, given: ZP = 6x-13, ZA = 9x+27, and AP = 3x +74.
#53-59
Geometry CC RHS Unit 1 Points, Planes, & Lines 28
59. A, B, and C are collinear with A between B and C. Draw a diagram and solve for x, given:
AC = 17x – 69, AB = 6x+23, and BC = 25x-50.
Congruence, Distance & Length: HOMEWORK
60. RV = 36 62. RV = 29 TV = 12 ST = UV ST = ? ST = TU = UV RS = 7 RS = ? UV = ? RS + ST = 16 RT = ?
61. RV = 36 63. RV = 27 TV = 12 SU = 6 ST = TU = UV ST = TU = UV RS = ? RS = ?, RU = ?
64. D, V, and U are collinear with U between D and V. Draw a diagram and solve for x, given: DU = 4x+5, VU = 3x-8, and VD = 10x-30. 65. P, R, and F are collinear with F between R and P. Draw a diagram and solve for x, given: FR = 7x-8, FP = 4x+20, and PR = 13x – 6. 66. W, S, and X are collinear with W between X and S. Draw a diagram and solve for x, given: XW = 3x+5, SW = 7x-18, and XS = 6x+19.
Constructions & Loci: CLASSWORK 67. Draw a circle for each given radius length in the figures below.
#60-66
Geometry CC RHS Unit 1 Points, Planes, & Lines 29
a) b)
68. Construct congruent segments for each segment given below. Hint: remember to draw a longer line in any direction to start constructing your congruent segment. a) b)
Constructions & Loci: HOMEWORK 69. Draw a circle for each given radius length in the figures below. a) b)
70. Construct congruent segments for each segment given below. Hint: remember to draw a longer line in any direction to start constructing your congruent segment. a) b)
Geometry CC RHS Unit 1 Points, Planes, & Lines 30
Geometry CC RHS Unit 1 Points, Planes, & Lines 31
PARCC type question:
71. The figure shows line j, point C on line j, and .
Part A:
Consider the partial construction of a line segment congruent to on line j. What would be the final step in the construction? a) Draw a point D between points C and A b) Draw a point D between points C and B c) Draw a point D on line j between point C and the given arc d) Draw a point D on line j at the given arc. Part B: Once the construction is complete, which of the following reasons listed contribute to providing the validity of the construction? a) Because the distance between A and D match the distance between B and C, AD = BC, making them congruent. b) Because the distance between A and C match the distance between B and D, AC = BD, making them congruent. c) Because the distance between A and B match the distance between C and D, AB = CD, making them congruent. d) Because the distance between A and j match the distance between B and D, Aj = BD, making them congruent.
AB
j
A
B
C
j
A
B
C
AB
Geometry CC RHS Unit 1 Points, Planes, & Lines 32
Points, Lines and Planes Review Multiple Choice
72. Intersecting lines are _________________ non-coplanar a. always b. sometimes c. never
73. Two non-parallel lines _________________ intersect at one point. a.always b.sometimes c.never
74. Two points are _________________ collinear. a.always b.sometimes c.never
75. Three points are _________________ collinear. a.always b.sometimes c.never
76. Three points are _________________ coplanar. a.always b.sometimes c.never
77. Four points are _________________ coplanar. a.always b.sometimes c.never
78. When two planes intersect, they do so: a.at a point b.along a line c.along a plane
79. All points along a line are _________________ collinear. a.always b.sometimes c.never
80. Opposite rays (circle all that apply): a.are collinear b.have the same endpoint
Geometry CC RHS Unit 1 Points, Planes, & Lines 33
c.sometimes overlap d.form a straight angle
81. Any two rays are ________ congruent. a. always b. sometimes c. never
82. Any two segments are ________ congruent. a. always b. sometimes c. never
For #70-74, use the diagram below.
83. Find the distance between point A and B.
a. 1 b. 2 c. 5 d. 10
84. Find the distance between point E and F.
a. 0.3 b. 0.6 c. 3 d. 6
85. Find the distance between point C and H.
a. 1.6 b. 1.8 c. 3 d. 3.4
86. Find the distance between point K and G.
a. 0.9 b. 3 c. 2.1 d. 21
87. Find the distance between point I and D.
a. 4 b. 4.1 c. 20.5 d. 41
Geometry CC RHS Unit 1 Points, Planes, & Lines 34
88. If points A, B, C are collinear with C between A and B, the segment addition postulate is: a.AB + BC = AC b.BA + CB = AC c.BC + CA = AB d.BC + AC = CA
89. Two rays that have a common endpoint could form (check all that apply): a. an angle b. a straight line c. opposite rays d. a vertex
90.The figure shows line k, point G on line k, and .
Part A:
Consider the partial construction of a line segment congruent to on line k. What would be the final step in the construction? a) Draw a point H on line k at the given arc. b) Draw a point H on line k between point G and the given arc c) Draw a point H between points F and G d) Draw a point H between points E and G Part B: Once the construction is complete, which of the following reasons listed contribute to providing the validity of the construction? a) Because the distance between F and G match the distance between E and H, FG = EH, making them congruent. b) Because the distance between E and F match the distance between G and H, EF = GH, making them congruent. c) Because the distance between E and G match the distance between F and H, EG = FH, making them congruent. d) Because the distance between G and k match the distance between G and H, Gk = GH, making them congruent.
EF
k
E
F
G
k
E
F
G
EF
Geometry CC RHS Unit 1 Points, Planes, & Lines 35
Points, Lines and Planes Review Constructed Response
91. Points J, K and L are collinear with J between L and K. KJ = 2x + 3, LK = 9x – 7 and LJ = 4x + 8. Draw a diagram, solve for x, and find the measures for KJ, LJ & LK.
92. Points B, D, F, H and J are collinear and are in the following order
D is between J and B
F is between D and J
B is between F and H
JH = 47, FB = 12, FD = DB = BH and JF = 3x - 7 Draw a diagram of the points, solve for x and solve for JF.
Geometry CC RHS Unit 1 Points, Planes, & Lines 36
Answer Key
1. KLI & HLJ 2. HLK, HLI, KLJ, ILJ 3. LK, LI, LJ, LH 4. 3 5. Infinite 6. VRS 7. QVW, TUR, QUS, VRS 8. RW, RU 9. TURW, j 10. Infinite 11. Q 12. Q 13. R 14. P 15. PSOU or R 16. O 17. U 18. O 19. U 20. POSQ or V 21. F 22. J 23. FHJI 24. ACJI 25. CH 26. A 27. J 28. F 29. EDJI 30. CHEJ 31. JI 32. D 33. 5 34. 12 35. 4 36. 3 37. 6 38. 14 39. 12 40. 17 41. 2.0 42. 0.6 43. 1.5 44. 2.3
45. 2.4 46. 3.7 47. 5.0 48. 3.5 49. 1.2 50. 1.3 51. 2.9 52. 5.0 53. 4 54. 12 55. ST=6 RS=11 SU=17 56. 5 57. 9 58. 5 59. 2 60. 6 61. 18 62. ST = 9 RS = 7 RT = 16 63. RS = 18 RU = 24 64. 9 65. 9 66. 8 67. Check Constructions 68. Check Constructions 69. Check Constructions 70. Check Constructions 71. Part A: choice d
Part B: choice c
Geometry CC UNIT 1 Points, Planes, & Lines 37
Review Answer Key Multiple Choice 72. C 73. A 74. A 75. B 76. A 77. B 78. B 79. A 80. A, B, D 81. A 82. B 83. A 84. B 85. D 86. C 87. B 88. C 89. A, B, C, D
90. Part A: A Part B: B
Geometry CC UNIT 1 Points, Planes, & Lines 38
Review Answer Key Constructed Response
91. x = 6, KJ = 15, LJ = 32, LK = 47
92. x = 12 JF = 29
Geometry CC UNIT 1 Points, Planes, & Lines 39
Prepared by : G. Alvarez-Garcia
UNIT 1
Basics of Geometry: Constructions, Points, Planes, &
Lines
Geometry CC
Geometry CC UNIT 1 Points, Planes, & Lines 40
1
2
Geometry CC UNIT 1 Points, Planes, & Lines 41
3
4
5
Geometry CC UNIT 1 Points, Planes, & Lines 42
6
7
Geometry CC UNIT 1 Points, Planes, & Lines 43
8
9
Geometry CC UNIT 1 Points, Planes, & Lines 44
10
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