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ADVANCED GEOMETRY: FALL 2015
SEMESTER REVIEW
On a separate sheet of paper, write a two-column algebra proof for the following problems.
1. Given: 3x + 12 = 8x – 18 Prove: x = 6
2. Given: 3(5x + 1) = 13x + 5 Prove: x = 1
3. Given: 6( x  4)  3  5 x  30  2 x Prove: x  3
Fill in the correct term to complete each sentence.
Two angles whose sum is 90  are _____________.
An angle that measures 120  is an _____________ angle.
Two angles whose measures have a sum of 180 are ___________.
Opposite rays form a ____________ and share an ____________.
The intersection of two planes is a ________________.
Adjacent angles share a _____________.
Vertical angles are ______________.
A segment bisector divides a segment into two _____ segments.
4)
5)
6)
7)
8)
9)
10)
11)
Refer to the figure at the right for questions #12 and #13.
U
-7
-6
-5
-4
-3
T
H
-2
-1
O
0
1
2
3
R
N
S
4
5
6
7
__________ 12. Find the length of UH .
__________ 13. Determine the midpoint of
TS
I. State whether each Postulate or Conjecture is TRUE (A) or FALSE (B).
_______________14) A plane contains at least 3 points all on the same line.
_______________15) A part of a line that consists of two points called endpoints, and all the points between
them can be termed a segment.
_______________16) Any plane can also be identified by a lower case script letter in the middle of the plane.
Use the figure below to answer the following questions.
______________17) Which of the following
represents an undefined term?
A.
CD
B.
___________
KF
C.
AC
D.
BCD
18) True or False
Points B, A, E form a plane.
For the following problems, choose the best
answer.
19) Find the best counterexample to show
that the following conjecture is false:
20) The squares below are arranged in a
sequence to show a pattern.
“Any three points that are coplanar are also
collinear.”
Each side of a square represents 1 unit. If this
pattern continues, what would be the perimeter
of the 8th figure?
A
14
A
A, C, and F are coplanar but not collinear.
B
20
B
A, E, and F are coplanar but not collinear.
C
24
C
A, B, and D are collinear but not coplanar.
D
There is no pattern
21) Which is not an example of deductive
reasoning?
22) Which statement does not have a
true contrapositive?
A
Coach Moyer is 25, therefore next year she
will be 26.
A If a polygon is a square, then it is a
quadrilateral.
B
If Filipe does this review, then he will pass.
C
Acute angles are less than 90 degrees.
If
A is 40 degrees, then A is acute.
B
If a vehicle has four wheels, then it is a
car.
C
If the sum of the measures of two
angles is 90 , then the angles are
complementary.
23.
Turtles don’t fly.
If-Then: __________________________________________________________T or F
Counterexample? ___________________________________
Converse: _________________________________________________________T or F
Counterexample? ___________________________________
Inverse: __________________________________________________________T or F
Counterexample? ___________________________________
Contrapositive: _____________________________________________________T or F
Counterexample?__________________________________
24.
If x = 4, then 2x+1 = 9.
Converse:
____________________________________________________________________________
Biconditional (if needed):
____________________________________________________________________________
Determine if the conclusion is valid.
If it is, state the law used (Law of Detachment or Law of Syllogism).
25. If it is December, Mr Valdes needs a break.
Mr Valdes needs a break.
Conclusion: It is December.
Valid? _______ Law (if valid): ______________________
26. If Miss Moyer is singing, then her students are actively engaged.
If her students are actively engaged, then they vote for her for Miss Dulles.
Conclusion: If Miss Moyer is singing, her students vote for her for Miss Dulles.
Valid? _______ Law (if valid): ______________________
State the law used (Law of Detachment or Law of Syllogism).
Write the conclusion.
27. If Miss Hays worked for the Astros, then she would give all of her students free tickets.
Miss Hays works for the Astros.
Law: _________________
Conclusion: __________________________________________________________
28. If Mrs Lucas is in a meeting, then you can’t go to tutorials. If you can’t go to tutorials, then you will fail
this exam.
Law: __________________
Conclusion: __________________________________________________________
In the figure at the right, WY bisects UV at Y and UY bisects TW at X .
the value of x and the measure of the indicated segment.
__________ 29.
For each situation, find
UV  x  6 , UY  x - 1; YV
T
__________ 30.
__________ 31.
TX  2x 1 , XW  x +7; TW
V
Y
X
U
WX  x  5 , TW  4x  5; TX
W
32. If BAT and EAT form a linear pair and BAT is obtuse, then EAT is
A. acute
B. obtuse
C. right
D. straight
33. Find mC if C  D, mC = 3x – 5, and mD = 2x + 5.
A. 36
B. 35
C. 20
D. 25
34. Find m1.
A. 35
C. 145
(4x+3)
B. 165
D. 15
1
(6x-13)
D
35. If mABD = 45 and mABC = 120, find mDBC.
A. 120
B. 75
C. 70
D. 80
A
B
36. If EB bisects AED and mDEB = 61, find mAED
A. 90
B. 180
C. 30
D. 122
B
C
C
D
A
E
37. In which diagram(s) are 1 and 2 supplementary?
I
IV
II
1
1
2
III
1
2
1
2
2
1
A.
B.
C.
D.
I only
II only
II and IV
I, III, and IV
38. If m1 = 7x – 5 and m2 = 5x + 27, what is the value of x?
A. 16
B. 32
C. 107
D. 73
1
2
39. 4 and 5 form a linear pair and m4 = 62. Find m5.
A. 62
B. 28
C. 118
D. 90
40. The measure of an angle is 38 degrees more than the measure of its complement. Find the measure of the
angle.
A. 26
B. 64
C. 71
D. 109
Using the diagram at the right, state a conclusion and give a justification
41. Given: DF bisects EDG
42. Given:
Conclusion:______________
Justification:____________
1  3
3  2
Conclusion: ________________
Justification:_________________
43. Given: E,F, G are collinear
And F is between E and G
Conclusion: _______________
44. Given: M is the midpoint of P and S
Conclusion:________________
Justification:______________
Justification:______________
45. Given: K is between J and L. JK = 6, KL = 10
Prove: JL = 16
Statements
Reasons
1. K is between J and L
1. ___________________________
2. JK = 6, KL = 10
2. ___________________________
3. _______________
3. ___________________________
4. __________
4. ___________________________
5. JL = 16
5. __Associative Property of addition_
46. Given: B is the midpoint of AC .
Prove:
BD  BC
BD  AB
Statements
1.
Reasons
BD  AB
1. ___________________________
2. B is the midpoint of AC
2. ___________________________
3.
AB  BC
3. ___________________________
4.
BD  BC
4. ___________________________
47. Given:
Prove:
WD
bisects CWK;
CWD KWM
Statements
1. WD bisects CWK
2. __________________
3.
WK
bisects DWM
WK
bisects DWM
Reasons
1. ___________________________
2. ___________________________
3. Given
4. __________________
4. ___________________________
5. __________________
5. ___________________________
48. a. Show 2 different ways on how congruent segments can be formed using a compass:
b. What does your teacher need to see in order to accept it as a correct answer?
c. Can you assume anything to be congruent?
From the figure on the right, match the angle pairs with their correct name.
49. _________
∠1 and ∠8
a. Same Side Interior
50. _________ ∠3 and ∠5
b. Corresponding
51. _________ ∠2 and ∠8
c. Alternate Exterior
52. _________ ∠4 and ∠5
d. Alternate Interior
53. _________ ∠3 and ∠7
e. Same Side Exterior
54. Use the diagram to answer the question.
Which statement proves that g || h?
A) 1  4
B) m5 + m7 = 180˚
C) 1  6
D) m2 + m8 = 180˚
55. Given the diagram, which statement and reason can be used to prove b || c?
b
a
c
1 4
2
3
5
6
7
8
A) 2  7, Alternate Exterior Angles Theorem
B) 2  6, Same Side Interior Angles Theorem
C) 1  4, Linear Pair Postulate
D) 1  3, Vertical Angles Theorem
Use the figure at the right for the next 4 questions.
56.Identify the special angle pair name for 10 and 6.
A. alternate interior
B. vertical
C. corresponding
D. alternate exterior
57. Given l m and m5 = 72, find m10.
A. 108
B. 72
C. 18
D. 112
58. Given lm , m11 = 9x + 5, and m3 = x + 37, find the value of x.
A. 32
B. 4
C. 41
D. 5
59. Given m8 = 5x - 2 and m9 = 3x + 70, find the value of x so that l m.
A. 16 B. 14
C. 62 D. 75
l
10
m
8 7
5 6
9
1 2
11
3
4
p
a
60. Find the value of x so that m n
A. 12
B. 20
C. 35
D. 40
117
b
3x+12
m
48
n
61. Fill in the blank for each of the following proofs.
Given: 1 
Prove: a b
c
2
1
2
a
3
b
Statements
Reasons
2 3
Transitive Property
a b
62. Given:
2 3
Prove: m 1  m 4  180
1
2
3 4
Statements
Reasons
1 2
m 1 m 2
3 and
4 are supplementary
Definition of Supplementary
Refer to the graph below to find each measure. If the measure is not a whole number, round to the
nearest hundredth.
63)
Find the distance between H and L. __________.
64) What is the distance between J and H? __________.
65) What is the measure of segment IN? ____________.
66)
Find the midpoint of NJ. ____________.
67)
F is the midpoint of EG. If EF = 2x + 3 and EG = 6x - 3, find FG.____________.
Find the slope of a line parallel AND perpendicular to the line passing through the given points.
68)
A (4, 1), B (2, 0)
______________
_____________
69)
C (2, -1), D (4, 2)
______________
_____________
70. Name the equation of the line whose slope = 5 , and y-intercept = 3/2?
A. y = ¾x – 3/2
B. y –2 = 5(x – 3)
C. y = 3/2x – 5
D. y = 5x + 3/2
71. Name the equation of the line whose slope = -¾, and passes through (-2, 5)?
A. y = -¾x – 5
B. y + 5 = -¾(x – 2)
C. y + 2= ¾(x – 5)
D. y –5 = -¾(x + 2)
72. Name the equation of the line through the points (2, 10) and (-2, 2)
A. y = 2x +10
B. y = ½ x +9
C. y = ½ x +10
D. y = 2x + 6
73. Name a point the line y + 1 = -2(x -4) passes through?
A. (-2, 1)
C. (-4, 2)
B. (4, -1)
D. (-4, 1)
74. Name the slope of the line y + 3 = -½(x - 1).
A. ½
B. –1/3
C. -½
D. 3/1
75. Name the equation of a line parallel to y = -4x + 9, passing through point (-2, 7)
A. y - 7 = -4(x + 2) B. y + 2 = ¼(x + 7)
C. y + 7 = 4(x – 2) D. y - 7 = -¼(x – 2)
76. Name the equation of the line perpendicular to y – 4 = 3(x - 8), with y-intercept = 6.
A. y = -1/3x + 6
B. y = 3x - 6
C. y = 1/3x - 4
D. y = -1/3x - 6
77. The vertices of ABC are A(2, 18), B(-2, -4), and C(6, 12)
Write the equation of the line containing the perpendicular bisector of BC .
1
A. y = 2x
B. y =  x – 5
2
1
C. y =  x + 5
D. y = 2x + 4
2
79. Which of the following is the graph of y + 1 =
A.
1
(x – 1)?
4
B.
C.
80. Which of the following is the graph of y = 2x + 3?
A.
B.
C.
D.
D.
81) Find the equation of the line that is the perpendicular bisector of the segment whose endpoints are (3, 7)
and (-3, -1).
Graph the three points given. Determine the equation of the line that is the median coming from ∠A.
82. ∠A (1, 5); ∠B (5, -1); ∠C (-1, 1)
83. ∠A (-2, -6); ∠B (0, 6); ∠C (2, 0)
Graph the three points given. Determine the equation of the line that is the perpendicular bisector of segment BC.
84. ∠A (-6, -5); ∠B (-1, -1); ∠C (-3, -3)
85. ∠A (5, 5); ∠B (-1, 4); ∠C (-3, -2)
86.
Find the value of x. The diagram is not to scale.
114°
45°
x°
A. 21
87.
B. 66
C. 45
D. 31
Find the value of x. The diagram is not to scale.
45
x
45
35
24
24
A. 90
B. 48
C. 35
D. 70
88. Which three lengths could be the lengths of the sides of a triangle?
A. 12 cm, 5 cm, 17 cm
C. 9 cm, 15 cm, 23 cm
B. 21 cm, 5 cm, 7 cm
D. 6 cm, 22 cm, 11 cm
89. A star patterned quilt has a star with the angles shown. What is the value of x? The diagram is not
to scale.
24°
xº
105°
A. 99
B. 105
C. 91
90. Points B, D, and F are midpoints of the sides of
The diagram is not to scale.
D. 81
EC = 30 and DF = 17. Find AC.
A
B
F
C
E
A. 30
D
B. 8.5
C. 60
D. 34
91.
Find the value of x.
14
2x – 9
A. 10
92.
B. 8
C. 7
Name the smallest angle of
D. 11.5
The diagram is not to scale.
C
8
9
7
A
B
A.
B.
C.
D. Two angles are the same size and
smaller than the third.
93.
What is the value of x?
32°
21
21
xº
Drawing not to scale
A. 158°
94.
B. 148°
C. 74°
D. 79°
List the sides in order from shortest to longest. The diagram is not to scale.
J
71°
84°
K
25°
L
A.
B.
C.
D.
Matching
For the next 5 questions, choose the Letter that matches the definition
A. Equilateral Triangle
D. Median
B. Isosceles Triangle
E. Altitude
C. Scalene Triangle
____ 95. A triangle with two sides congruent and base angles congruent
____ 96. A segment that connects a vertex of triangle with the midpoint of the opposite side
____ 97. A triangle with all sides congruent and all angles congruent
____ 98. A segment that connects a vertex of a triangle with the opposite side and is perpendicular to the
opposite
____ 99. A triangle with no sides congruent
____ 100. Name a median for
|
A
E
)
|
D
)
C
A.
F B
B.
C.
D.
____ 101. Which three lengths CANNOT be the lengths of the sides of a triangle?
A. 21 m, 8 m, 11 m
C. 25 m, 21 m, 11 m
B. 7 m, 10 m, 6 m
D. 15 m, 10 m, 15 m
____ 102.
Two sides of a triangle have lengths 5 and 12. Which inequalities represent the possible lengths
for the third side, x?
A.
C.
B.
D.
Find the length of the missing side. The triangle is not drawn to scale.
17
____ 104.
A. 4
15
B. 8
C. 64
D. 23
Matching
For the next 5 questions, match the letter to the correct definition
A. Orthocenter
D. Circumcenter
B. Incenter
E. Midsegment
C. Centroid
____ 105.
The point of concurrency of Altitudes of a triangle
____ 106.
A segment that connects the midpoints of two sides of a triangle
____ 107.
The point of concurrency of Medians of a triangle
____ 108.
The point of concurrency of Perpendicular Bisecters of a triangle
____ 109.
The point of concurrency of Angle Bisectors of a triangle
B
110. The coordinates of the image of ABC after a reflection over the
y-axis are:
A. A(5,-1), B(4,-7), C(1,-3)
B. A(-5,1), B(-4,7), C(-1,3)
C. A(-1,-5), B(-7,-4), C(-3,-1)
D. A(-1,5), B(-7,4), C(-3,1)
C
A
111. A transformation is described in the equation (x,y) = (3x, ½y). Which of the following best
describes what the transformation does to the geometric figure?
A. enlargement
B. reduction
C. horizontal stretch and vertical shrink
D. horizontal shrink and vertical stretch
113. The coordinates of the image of quadrilateral DEFG after a
slide of 2 units up and 3 units left are:
A. D(4,2), E(6,-2), F(0,-8), G(-2,-4)
B. D(0,8), E(2,4), F(-4,-2), G(-2,-2)
C. D(5,3), E(7,-1), F(1,-7), G(-1,-3)
D. D(-1,7), E(1,3), F(-5,-3), G(-7,1)
D
E
G
F
114. Find the coordinates of the image of the point with coordinates (3,6) after a rotation of 270
A. (6,-3)
B. (-6,3)
C. (–3,-6)
D. (3,-6)
115. The dashed triangle is the image of the solid triangle.
What is the scale factor?
A. ½
B. 3
C. 1/3
D. 2
116. The line y = 3x + 6 is reflected over the y-axis. What is the equation of the reflection?
A. y = -3x + 6
B. y = -3x – 6
C. y = 3x – 6
D. y = (1/3)x + 6
117. Which of the following transformations would preserve the slopes of lines?
I.
Translations
II. 180 rotation
III. Dilation
IV. Reflection over the y-axis
V. Distortion
A.
B.
C.
D.
I, IV, and V
II and III
I, II, and III
I-V
118)
x 3
4

2 x  1 22
x2 7

x3 2
119)
120)
x 1 x 1

5
2
121) On a map showing the mythical land of Nordtor, 1.2 cm represents 24 km. On the map, it is
approximately 5 cm from Foust Knight Rock to Brigham Storm Bay on the map. What is the
distance in kilometers?
_________________________
122) A 15 foot building casts a 9 foot shadow.
same time?
How tall is a building that casts a 30 foot shadow at
actual
the
GIVEN: Similar Trapezoids ABCD and EFGH:
B
4
F
G
H
C
2
6
5
E
A
8
D
123) a) What is the ratio of the perimeters of the trapezoids shown?
__________________
b)
Find the perimeter of trapezoid GHEF.
__________________
B
Given ABC ~ EFG, solve the following problems.
F
E
A
G
C
124) If the perimeter of ABC is 36, the perimeter of EFG is 12, given that BC is 12, find the measure of FG.
__________________