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Transcript
```Angles
Angles: CLASSWORK
Classify each angle using all of the names that apply: acute, right, obtuse, straight, or reflex.
1.
2.
3.
I
16°
180°
Y
X
K
J
Z
U
V
240°
W
Determine if each statement below is always, sometimes, or never true.
4. An angle that measures 90 degrees is ____________ an acute angle.
5. An angle that is more than 90 degrees is _____________ obtuse.
6. The interior of an angle is ______________ located outside of the angle.
7. An obtuse angle is _____________ considered to be a reflex angle.
Angles: HOMEWORK
8.
9.
O
10.
L
R
90°
120°
P
Q
S
N
M
344°
T
Determine if each statement below is always, sometimes, or never true.
11. An obtuse angle is ____________ considered to be a straight angle.
12. An angle that is less than 90 degrees is _____________ straight.
13. The exterior of an angle is ______________ located outside of the angle.
14. A reflex angle is _____________ considered to be an obtuse angle.
Congruent Angles: CLASSWORK
Determine if each pair of angles are congruent. If so, write a congruence statement. If not, explain why.
15.
16.
17.
B
H
C
E
F
I
D
52°
K
J
L
G
F
Z
E
51°
M
B
D
A
Congruent Angles: HOMEWORK
Determine if each pair of angles are congruent. If so, write a congruence statement. If not, explain why.
18.
19.
20.
N
T
Q
R
S
Geometry - Angles
O
P
U
60°
V
X
~1~
J
E
W
60°
Y
F
G
H
I
NJCTL.org
Angles & Angle Addition Postulate: CLASSWORK – For #21-25, find the missing angle measure.
21.
#106
22. #107
24.#109
25.
#110
26.
111.
23.#108
27.
112.
28.
113.
Geometry - Angles
~2~
NJCTL.org
Angles & Angle Addition Postulate: HOMEWORK – For #29-33, find the missing angle measure.
29.
30.
31.
32.
34.
33.
35.
36.
Geometry - Angles
~3~
NJCTL.org
PARCC-type question:
37. The figure shows the lines h, k, j, and ray g intersecting to form the angles numbered 1, 2, 3, 4, 5, 6, and 7.
All of the lines and ray are in the same plane. Based on the figure, which of the individual statements would
provide enough information to concluded that line k is perpendicular to line j? Circle all that apply.
h
k
7
6
g
12
3
54
a.
b.
c.
d.
e.
f.
mÐ3 + mÐ4 = 90°
mÐ3 = 90°
mÐ1 + mÐ7 = 90°
mÐ6 + mÐ7 = 90°
mÐ1 = mÐ4
mÐ4 = 90°
j
Protractors: CLASSWORK
Figure for #38 - 49
Use the figure above to find the measurement of each angle.
38. mÐAHB =
39. mÐAHG =
40. mÐAHF =
41. mÐBHE =
42. mÐCHF =
43. mÐDHE =
Protractors: HOMEWORK
Use the figure above to find the measurement of each angle.
44. mÐAHE =
45. mÐFHG =
46. mÐBHG =
47. mÐAHD =
48. mÐCHE =
49. mÐDHF =
Geometry - Angles
~4~
NJCTL.org
Special Angle Pairs: CLASSWORK
50. True/False: Complementary angles form a right angle
51. True/False: Supplementary angles form a straight angle
52. Two angles are complementary. One of the angles is 17°, what is the measure of the other angle?
53. Two angles are supplementary. One of the angles is 97°, what is the measure of the other angle?
54. Two angles are supplementary. One of the angles is three times the size of the other, what is the
measure of the larger angle?
55. An angle x is 20° more than its complement. What is the angle’s measure?
56. An angle x is 66° less than its complement. What is the angle’s measure?
57. An angle x is 46° more than its supplement. What is the angle’s measure?
58. An angle x is 18° less than its supplement. What is the angle’s measure?
Special Angle Pairs: HOMEWORK
59. True/False: Supplementary angles always sum to 90°
60. True/False: Complementary angles sometimes form straight angles
61. Two angles are complementary. One of the angles is 57°, what is the measure of the other angle?
62. Two angles are supplementary. One of the angles is 43°, what is the measure of the other angle?
63. Two angles are supplementary. One of the angles is five times the smaller angle, what is the measure
of the larger angle?
64. An angle is 74° more than its complement. What is the angle’s measure?
65. An angle is 36° less than its complement. What is the angle’s measure?
66. An angle is 88° more than its supplement. What is the angle’s measure?
67. An angle is 16° less than its supplement. What is the angle’s measure?
Geometry - Angles
~5~
NJCTL.org
Proofs of Special Angles: CLASSWORK
Find the measures of the missing angles.
68.
69.
Find the value of the variables.
70.
71.
72.
73.
74.
75.
Geometry - Angles
~6~
NJCTL.org
Proofs of Special Angles: HOMEWORK
Find the measures of the missing angles.
76.
77.
33° 4
5 6
Find the value of x.
78.
79.
80.
81.
82.
83.
Geometry - Angles
~7~
NJCTL.org
Angle Bisector: CLASSWORK
Given that ray BD bisects ∠ ABC in the figure below, find the missing measurements. Note: the questions are
NOT related.
84.
85.
86.
87.
Given that ray JL bisects ∠ IJK in the figure below, find the value of x.
88.
89.
90.
91.
Geometry - Angles
~8~
NJCTL.org
Angle Bisector: HOMEWORK
Given that ray RT bisects ∠ QRS in the figure below, find the missing measurements. Note: the questions are
NOT related.
93.
92.
R
Q
S
94.
95.
T
Given that ray JL bisects ∠ IJK in the figure below, find the value of x.
96.
97.
98.
99.
Geometry - Angles
~9~
NJCTL.org
Locus & Angle Constructions: CLASSWORK
10. Construct a congruent angle for each figure below.
a)
A
B
C
b)
D
E
F
Locus & Angle Constructions: HOMEWORK
101. Construct a congruent angle for each figure below.
a)
H
G
I
b)
K
J
L
Geometry - Angles
~10~
NJCTL.org
Angle Bisectors & Constructions: CLASSWORK
102. Construct the angle bisector of each angle below using any construction method of your choice.
a)
b)
Angle Bisectors & Constructions: HOMEWORK
103. Construct the angle bisector of each angle below using any construction method of your choice.
a)
b)
PARCC type question:
104. The figure below shows angle NOP.
Consider the partial construction of a ray that would
bisect angle NOP. What would be the final step in
the construction?
a) Draw a ray starting at point P going through
point T.
b) Draw a ray starting at point N going through
point T.
c) Draw a ray starting at point O going through
point T.
d) Draw a ray starting at point R going through
point T.
N
O
P
Part A:
Part B:
Once the construction is complete, which of the
following reasons listed contribute to providing the
validity of the construction?
N
T
Q
O
R
Geometry - Angles
a)
b)
c)
d)
P
~11~
mÐNQT = mÐNOP
mÐQNT = mÐNOP
mÐTRP = mÐNOP
mÐNOT = mÐPOT
NJCTL.org
Angles
Review Multiple Choice
105.
Opposite rays (circle all that apply):
a.are collinear
b.have the same endpoint
c.sometimes overlap
d.form a straight angle
106.
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
107.
Acute angles are:
a. less than 90°
b. greater than 90° but less than 180°
c. equal to 180°
d. greater than 180° but less than 360°
108.
Obtuse angles are:
a. less than 90°
b. greater than 90° but less than 180°
c. equal to 180°
d. greater than 180° but less than 360°
109.
Adjacent angles (circle all that apply):
a. have a common side
b. sum to 90°
c. share a common vertex
d. are less than 90°
110.
Complementary angles (circle all that apply):
a. sum to 90°
b. sum to 180°
c. form a straight angle
d. form a right angle
111.
Supplementary angles (circle all that apply):
a. sum to 90°
b. sum to 180°
c. form a straight angle
d. form a right angle
Geometry - Angles
~12~
NJCTL.org
112.
An angle measures 34°. What is the measure of its supplement?
a. 56°
b. 66°
c. 156°
d. 146°
113.
An angle measures 58°. What is the measure of its complement?
a. 22°
b. 32°
c. 42°
d. 122°
114.
Find the measures of the angles to the right.
a.
b.
c.
d.
1 113°
2 3
115.
Find the value of x in the figure to the right.
a. ½
b. 9
(x+19)°
c. 12
d. 24
(5x+17)°
116.
An angle bisector (circle all that apply):
a. forms two congruent angles
b. is a line or a ray
c. is equidistant from the sides of the angle
117.
The statement, "the whole is the sum of the parts" refers to (circle all that apply):
a. complementary angles
118.
Ray RT bisects ∠QRS. If m∠QRT = 33°, what are the measurements of the remaining two angles?
a. m∠TRS = 33°, m∠QRS = 33°
b. m∠TRS = 66°, m∠QRS = 66°
T
c. m∠TRS = 33°, m∠QRS = 66°
Q
d. m∠TRS =66°, m∠QRS = 33°
119.
Ray OL bisects ∠NOP. Find the value of x.
a. 2
N
b. 4.8
c. 6.5
(5x + 16)°
d. 9
O
Geometry - Angles
~13~
R
S
L
(8x - 11)°
P
NJCTL.org
120.
The figure shows the o, p, and q intersecting to form the angles numbered 1, 2, 3, 4, 5, and 6. All of
the lines are in the same plane. Based on the figure, which of the individual statements would
provide enough information to concluded that line o is perpendicular to line q? Circle all that apply.
p
q
1 23
6 54
o
121.
a.
b.
c.
d.
e.
f.
mÐ3 + mÐ4 = 90°
mÐ3 = 90°
mÐ5 + mÐ6 = 90°
mÐ4 + mÐ5 = 90°
mÐ3 = mÐ6
mÐ4 = 90°
The figure below shows angle ACE.
A
C
E
Part A:
A
F
B
C
D
E
Consider the partial construction of a ray that would bisect angle ACE. What would be the final step
in the construction?
a. Draw a ray starting at point D going through point F.
b. Draw a ray starting at point C going through point F.
c. Draw a ray starting at point B going through point F.
d. Draw a ray starting at point A going through point F.
Part B:
Once the construction is complete, which of the following reasons listed contribute to providing the
validity of the construction?
a. mÐACF = mÐECF
b. mÐABF = mÐACE
c. mÐFDE = mÐACE
d. mÐACE = mÐBAF
Geometry - Angles
~14~
NJCTL.org
Angles
Review Constructed Response
122. An angle is 36° less than its complement. What is the measure of the angle?
123. An angle is 102° more than its supplement. What is the measure of the angle?
124. If F is in the interior of ∠APB and m∠APB = (5x +11)°, m∠APF = (6x – 6)° and m∠FPB = (9x – 23)°:
 Draw a diagram
 Solve for x
 What is the m∠FPB, m∠APF and m∠APB?
Geometry - Angles
~15~
NJCTL.org
1. Acute
2. Obtuse, straight
3. Obtuse, reflex
4. Never
5. Always
6. Never
7. Sometimes
8. Right
9. Obtuse
10. Obtuse, reflex
11. Sometimes
12. Never
13. Always
14. Always
15. Yes ∠BCD ≅ ∠EFG
16. No; angle measures are
not equal
17. No; not enough info
18. No; not enough info
19. Yes; ∠TUV ≅ ∠WXY
20. No; angle measures are
not equal
21. 26°
22. 72°
23. 23°
24. 123°
25. 193°
26. 15
27. 3
28. 3
29. 71°
30. 14°
31. 17°
32. 57°
33. 33°
34. 5.8666...
105.
106.
107.
108.
109.
110.
111.
112.
A, B, D
A, B, C, D
A
B
A, C
A, D
B, C
D
Geometry - Angles
35. 2
36. 7
37. b & d
38. 30°
39. 180°
40. 155°
41. 90°
42. 107°
43. 120°
44. 97°
45. 25°
46. 150°
47. 83°
48. 72°
49. 72°
50. True
51. True
52. 73°
53. 83°
54. 135°
55. 55°
56. 12°
57. 113°
58. 81°
59. False
60. False
61. 33°
62. 137°
63. 150°
64. 82°
65. 27°
66. 134°
67. 82°
68. 63°, 117°, 63°
69. 128°, 128°, 52°
70. x = 17
71. x = 7
72. x = 16
73. x = 13
74. x = 16 & y = 6
75. x = 4 & y = 6
76. 126°, 54°, 54°
77. 147°, 147°, 33°
78. x = 11
79. x = 7
80. x = 13
81. x = 10
82. x = 20 & y = 5
83. x = 10 & y = 20
84. 39°, 39°
85. 44°, 44°
86. 112°, 56°
87. 46°, 92°
88. x = 24
89. x = 6
90. x = 10
91. x = 9
92. 48°, 96°
93. 88°, 176°
94. 83°, 83°
95. 53°, 53°
96. x = 10
97. x = 21
98. x = 8
99. x = 4.5
100.
Check
Constructions
101. Check Constructions
102. Check Constructions
103. Check Constructions
104. Part A: c
Part B: d
113. B
114. C
115. D
116. A, B, C, D
117. B, D
118. C
119. D
120. B, D
~16~
NJCTL.org
121. Part A: B
Part B: A