Download Geo REVIEW for Final Exam sem 1 part A worked out answers

Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
1. PS = 20.2 mm, RS = 13.6 mm
Geo REVIEW for Final Exam – Semester 1 S
R
P
Part A
PR = _____
2. Find the value of a if M is between L and N.
LM = 8a, MN = 7a, LN = 75 ft
SKETCH:
Use the figure to the right to answer the following questions.
3. Name the angle which is vertical to ÚABU _________ Which angle is vertical to ÚQBT _________
Q
A
T
B
U
a = _____
LM = _____
C
E
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Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
Use the figure to the right to answer the following questions.
Use the figure to the right to answer the following questions.
4. Find the measure of ÚABU that proves ÚABU and ÚQBA are
complementary if ÚABU is twice ÚQBA. Write an equation and solve by showing all work.
5. If mÚQBT = 9x + 54, find the value of x given that QB ¼ BT. Show all your work. Q
A
Q
A
T
B
U
T
B
U
E
C
mÚABU = _________ Use the figure to the right to answer the following questions.
Use the figure to the right to answer the following questions.
6. If mÚABQ = 5x – 4 and mÚQBE = 6x + 8, find x and mÚABQ by writing an equation and showing all work. Q
A
7. If mÚUBE = 6x + 17 and mÚEBT = 4x – 8, find x by writing an equation and showing all work. Q
A
T
B
U
T
B
U
C
x = ________ and mÚABQ = __________
E
C
x = _______
E
C
E
x = ________ and mÚEBT = __________
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Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
9. Use the figure at the right. U
If mÚEFD = 30, find mÚAFD = _________
and mÚBFC = _________ 3y ­ 1
3x ­ 2
T
Z
2x + 3
A
2y + 6
V
B
F
W
E
D
G
C
x = ________ and y = ________ 10. Use the figure at the right. If mÚAFE = 9x – 20, and mÚBFA = 3x + 5, find x by
writing an equation and showing all work.
11. Use the figure at the right. A
B
F
If mÚGFC = 29, find mÚGFD.
A
D
x = _______
G
B
F
E
C
mÚGFD = _______
E
D
G
C
3
Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
12. Refer to the figure to answer the following questions. Identify the special name for each pair of angles. a) Ú1 and Ú3 r
_______________________________
b) Ú5 and Ú16 1 2
4 3
5 6
8 7
9 10
12 11
13 15
14 16
_______________________________ p
q
transversal ____
s
______________________________ transversal ____
d) Ú3 and Ú9 _______________________________ ______________________________ c) Ú8 and Ú13 12. Refer to the figure to answer the following questions. Identify the special name for each pair of angles. r
1 2
4 3
transversal ____
5 6
8 7
e) Ú2 and Ú3 transversal ____
s
9 10
12 11
13 15
14 16
p
q
14. Given p Ç q and mÚ9 = 94, 13. Given p Ç q and mÚ3 = 62,
r
find mÚ5 = __________ 1 2
4 3
find mÚ2 = __________ find mÚ1 = __________ find mÚ8 = __________
s
5 6
8 7
9 10
12 11
13 15
14 16
p
q
find mÚ13 = __________ r
find mÚ15 = __________ find mÚ12 = __________ find mÚ16 = __________
s
1 2
4 3
5 6
8 7
9 10
12 11
13 15
14 16
p
q
4
Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
15. If p Ç q by the Consecutive Interior Angles Theorem, which angle pair must be supplementary?
Ú_____ and Ú_____ r
1 2
4 3
Ú_____ and Ú_____ Ú_____ and Ú_____ Ú_____ and Ú_____ s
Refer to the figure below to answer the following questions.
16. Given mÚ1 = mÚ5, which postulate or theorem justifies that s Ç t?
s
5 6
8 7
9 10
12 11
13 15
14 16
p
q
t
1 2
3 4
5 6
7 8
Refer to the figure below to answer the following questions.
Refer to the figure below to answer the following questions.
17. Given mÚ3 = mÚ6, which postulate or theorem justifies that s Ç t?
18. Given mÚ2 = mÚ7, which postulate or theorem justifies that s Ç t?
s
t
1 2
3 4
5 6
7 8
s
t
1 2
3 4
5 6
7 8
5
Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
Refer to the figure below to answer the following questions.
19. Given mÚ4 + mÚ6 = 180, which postulate or theorem justifies that s Ç t?
s
t
20. Find the value of x so that a Ç b. Write an equation and solve by showing all work. 1 2
3 4
(3x + 38)¡ a
5 6
7 8
(6x ­ 10)¡ b
21. Find the value of x AND explain which theorem you used and why. Write an equation and solve by showing all work.
22. In the figure at the right mÚIJK = 121°, mÚIJE = 37¡, and mÚEJK = 3x + 12. Find x
K
(3x + 17)¡ x = ________ J
E
(5x ­ 7)¡ I
x = ________ 6
Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
24. Classify each TRIANGLE twice: Once by its SIDES, and once by its ANGLES.
23. Find the mÚ1. 46¡ 1 24. Classify each TRIANGLE twice: Once by its SIDES, and once by its ANGLES.
24. Classify each TRIANGLE twice: Once by its SIDES, and once by its ANGLES.
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Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
25. Given èRST is isosceles and has a base angle of 27¡, find the measure of its vertex angle. 26. Use the figure at the right to find the value of x. Explain which theorem you used and why. Show all your work.
D
7x ­ 2
E
Vertex angle = _______ ° 27. Use the figure at the right to find the value of x given mÚ2 = 3x – 4. Show all your work.
F
5x + 8
150¡ B
28. Use the figure at the right to find x and then the length of a side of this equilateral triangle.
Show all your work.
2
35¡ 2x + 13
4x ­ 1
6x ­ 15
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Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
29. Find the measure of the indicated angles.
30. Find the measure of the indicated angles.
70¡ 70¡ 2
1
60¡ 3 4
2
Ú1 = __________ Ú3 = __________
1
40¡ Ú2 = __________ Ú4 = __________
Ú1 = __________
40¡ 3
Ú2 = __________
Ú3 = __________
31. Point K(–2, 1) is rotated 90° about the origin. What are the coordinates of K′?
( ____ , ____ )
32. Point A(1, –4) is rotated 180° about the origin. What are the coordinates of A’?
( ____ , ____ )
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Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
33. Point B(–2, –2) is rotated 270° about the origin. What are the coordinates of B’?
( ____ , ____ )
34. Point T(–2, 1) is reflected in the x­axis. What are the coordinates of T′?
Then explain HOW you got your answer. ( ____ , ____ )
35. Point R(1, –4) is reflected in the y­axis. What are the coordinates of R’?
36. Name the reflection of point S in line m. Then explain HOW you got your answer. 37.
T
m
U
38.
V
X
( ____ , ____ )
39.
R
S
W
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Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
40. What is the image of Y(–2, 1) under the translation〈5, 3〉? 42. If a 4” wide by 6” long picture is enlarged to 10” wide what is
the scale factor? ( ____ , ____ )
41. What is the image of P(1, –8) under the translation 〈–2, 4〉? 43. If the number of pixels on my screen were increased from ( ____ , ____ )
1200 to 1500 what is the scale factor of the enlargement? 44.
What kind of transformation is represented in the figure below?
45. What vector best describes the translation
in the figure below?
y
A
A
A'
x
B'
B
A'
C'
C
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Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
46. Translation: __________ a figure a distance horizontally and a distance vertically. 49. If èDJL ¤ èEGS, which segment in èEGS corresponds to
to ÚJLD? __________
47. Reflection: __________ a figure across a line in the direction perpendicular to the line of refection.
48. Rotation: __________ a figure by moving it about a point, along an arc through a specified angle.
50. Quadrilateral MNQP is made of two congruent triangles. bisects ÚMNQ and ÚMPQ. In the quadrilateral, mÚMNQ = 40 and mÚMPQ = 120. What is the measure of ÚM?
N
a)
b)
c)
Q
M
mÚM = ________
51. Given a drawing with congruent parts marked, state which triangle congruence theorem would prove the triangles congruent. It is ok to assume that common parts and vertical angles are congruent.
P
12
Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
51. Given a drawing with congruent parts marked, state which triangle congruence theorem would prove the triangles congruent. It is ok to assume that common parts and vertical angles are congruent.
d)
52.
e)
Y
53. Which triangles are congruent in the figure? And by what Theorem?
M
N
H
G
A
A
D
B
C
F
E
D
a) ____________________
b) ____________________
By _________________ By _________________ Q
P
N
S
R
T
____________________
By _________________ 13
Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
54. State the ANGLES of each triangle from Smallest to Largest & state the SIDES from Shortest to Longest.
54. State the ANGLES of each triangle from Smallest to Largest & state the SIDES from Shortest to Longest.
F
a)
B
b)
9
E 3
M
7
D
A
Ú ___, Ú ___, Ú ___ ____ , ____ , ____ 74¡ 22¡ 84¡ 27
d) P
c)
85¡ C
49¡ 11
17
N
Q
R
L
Ú ___, Ú ___, Ú ___ ____ , ____ , ____ Ú ___, Ú ___, Ú ___ Ú ___, Ú ___, Ú ___ ____ , ____ , ____ ____ , ____ , ____ Refer to the figure at the right to answer the following questions.
55. Name an angle bisector. _________ 59. Name an angle bisector. _________ (should be a ray!) (should be a ray!) 56. Name a median. __________ (should be a segment)
57. Name an altitude. ____________ (should be a segment)
B
G
60. Name a median. __________ H
(should be a segment)
A
DE
F
C
61. Name an altitude. ____________ (should be a segment)
58. Name a perpendicular bisector. _____________ ( should be a line) 62. Name a perpendicular bisector. _____________ ( should be a line)
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Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
64. If is a median, then which statement is TRUE?
63. Given: is an altitude, which of the following is a TRUE statement?
a) ÚDGF is a right angle
a) ÚYWZ is a right angle
b) ÚXYW ¤ ÚZYW
c) DG = GE
c) XW = WZ
b) DF = EF
d) ÚDFG ¤ ÚEFG
d) XY = ZY
D
X
G
Y
W
E
Z
65. If is a perpendicular bisector, then complete 5 TRUE statements.
D
a) Ú_____ is a right angle c) _____ is a midpt of _____
66. Given: Quadrilateral VWXY is a parallelogram V
Prove: VZ = ZX and YZ = ZW
G
b) DG = _____ E
F
W
Z
Y
F
Statements
X
Reasons
e) Ú_____ is a right angle 15
Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
Y
67. Given: ÚY¤ÚW, Z is the midpoint of XT Prove: èYXZ ¤ èWTZ
T
Z
68.
Write an equation of a line parallel to the line. X
W
69.
Write an equation of a line perpendicular to the line.
Graph the lines on the coordinate plane to the right.
70.
Write an equation in slope–intercept form for the line that satisfies the given conditions. Show work!
73. through (–4, 2), parallel to the line y = –4x +1. 71.
72. Are the lines from #70 and #71 parallel, perpendicular, or neither.
EXPLAIN how you got your answer.
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Geo REVIEW for Final Exam sem 1 part A worked out answers.notebook December 13, 2016
Write an equation in slope–intercept form for the line that satisfies the given conditions. Show work!
75. Choose ALL the lines perpendicular to y = 5x – 3. _____ a) y = –0.2x + 8 74. through (2, –6), perpendicular to the line y = 2x – 3.
_____ b) y = –5x + 3 _____ c) y – 1 = –4(x + 2) _____ d) y = 5
Find the value of x for each figure.
Find the value of x for each figure.
76.
77.
x
122¡ 67¡ x
17