Download NAME: - Fort Bend ISD

ADVANCED GEOMETRY: FALL 2016
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.
4)
5)
6)
7)
8)
9)
10)
11)
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.
I. State whether each Postulate or Conjecture is TRUE (A) or FALSE (B).
_______________12) A plane contains at least 3 points all on the same line.
_______________13) A part of a line that consists of two points called endpoints, and all the points between
them can be termed a segment.
_______________14) Any plane can also be identified by a lower case script letter in the middle of the plane.
15) Find the best counterexample to show
that the following conjecture is false:
“Any three points that are coplanar are also
collinear.”
A
A, C, and F are coplanar but not collinear.
B
A, E, and F are coplanar but not collinear.
C
A, B, and D are collinear but not coplanar.
16) Which is not an example of deductive
reasoning?
17) 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.
A is 40 degrees, then A is acute.
If
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.
18.
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?__________________________________
State the law used (Law of Detachment or Law of Syllogism).
Write the conclusion.
19. 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: __________________________________________________________
20. 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: __________________________________________________________
21. Find mC if C  D, mC = 3x – 5, and mD = 2x + 5.
A. 36
B. 35
C. 20
D. 25
22. Find m1.
A. 35
C. 145
(4 1 (6
x
x+
1
3)
3)


D
A
B
B. 165
D. 15
23. If mABD = 45 and mABC = 120, find mDBC.
A. 120
B. 75
C. 70
D. 80
24. If EB bisects AED and mDEB = 61, find mAED
A. 90
B. 180
C. 30
D. 122
B
A
C
C
D
E
25. In which diagram(s) are 1 and 2 supplementary?
I
IV
12
A.
B.
C.
D.
I only
II only
II and IV
I, III, and IV
12
12
II
1
2
III
1
26. If m1 = 7x – 5 and m2 = 5x + 27, what is the value of x?
A. 16
B. 32
C. 107
D. 73
27. 4 and 5 form a linear pair and m4 = 62. Find m5.
A. 62
B. 28
C. 118
D. 90
1
2
28. 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. ___________________________
30. 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.
31. _________
∠1 and ∠8
a. Same Side Interior
32. _________ ∠3 and ∠5
b. Corresponding
33. _________ ∠2 and ∠8
c. Alternate Exterior
34. _________ ∠4 and ∠5
d. Alternate Interior
35. _________ ∠3 and ∠7
e. Same Side Exterior
36. 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˚
37. Given the diagram, which statement and reason can be used to prove b || c?
a
b
c
14
23 57
68
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.
l
38. Identify the special angle pair name for 10 and 6.
A. alternate interior
B. vertical
C. corresponding
D. alternate exterior
87
1
56
1029
1
34
1
39. Given l m and m5 = 72, find m10.
A. 108
B. 72
C. 18
D. 112
40. 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
41. 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
a
42. Find the value of x so that m n
A. 12
B. 20
C. 35
D. 40
1
1
7

b
3
x
4
+
18
2
m
n
m
p
Refer to the graph below to find each measure. If the measure is not a whole number, round to the
nearest hundredth.
43)
Find the distance between H and L. __________.
44) What is the distance between J and H? __________.
45) What is the measure of segment IN? ____________.
46)
Find the midpoint of NJ. ____________.
47) 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.
48)
A (4, 1), B (2, 0)
______________
_____________
49)
C (2, -1), D (4, 2)
______________
_____________
50. 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
51. 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
52. Name the slope of the line y + 3 = -½(x - 1).
A. ½
B. –1/3
C. -½
53. Which of the following is the graph of y = 2x + 3?
A.
B.
D. 3/1
C.
D.
54.
Find the value of x. The diagram is not to scale.
114°
45°
x°
A. 21
55.
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
56. 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
57. Points B, D, and F are midpoints of the sides of
The diagram is not to scale.
EC = 30 and DF = 17. Find AC.
A
B
F
C
E
A. 30
D
B. 8.5
C. 60
D. 34
58.
Find the value of x.
14
2x – 9
A. 10
59.
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.
60.
C.
D. Two angles are the same size and
smaller than the third.
What is the value of x?
32°
21
21
xº
Drawing not to scale
A. 158°
B. 148°
C. 74°
D. 79°
61.
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
____ 62. A triangle with two sides congruent and base angles congruent
____ 63. A segment that connects a vertex of triangle with the midpoint of the opposite side
____ 64. A triangle with all sides congruent and all angles congruent
____ 65. A segment that connects a vertex of a triangle with the opposite side and is perpendicular to the
opposite
____ 66. A triangle with no sides congruent
____ 67. Name a median for
|
A
E
)
|
D
)
C
A.
F B
B.
C.
D.
____ 68. 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.
Matching
For the next 5 questions, match the letter to the correct definition
A. Orthocenter
D. Circumcenter
B. Incenter
E. Midsegment
C. Centroid
____ 69. The point of concurrency of Altitudes of a triangle
____ 100.
A segment that connects the midpoints of two sides of a triangle
____ 101.
The point of concurrency of Medians of a triangle
____ 102.
The point of concurrency of Perpendicular Bisecters of a triangle
____ 103.
The point of concurrency of Angle Bisectors of a triangle
104. 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)
B
C
A
105. 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
106. The coordinates of the image of quadrilateral DEFG after a
D
slide of 2 units up and 3 units left are:
A. D(4,2), E(6,-2), F(0,-8), G(-2,-4)
E
G
B. D(0,8), E(2,4), F(-4,-2), G(-2,-2)
F
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)
107. 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)
108. 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. I, IV, and V
B. II and III
C. I, II, and III
D. I - V
GIVEN: Similar Trapezoids ABCD and EFGH:
B
4
C
F
G
H
5
2
6
A
E
8
D
109) 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
A
C
E
G
110) If the perimeter of ABC is 36, the perimeter of EFG is 12, given that BC is 12, find the measure of FG.
__________________.
111. If BCDE is congruent to OPQR, then
is congruent to ________.
A.
B.
112. Given
A. 22
C.
and
B. 11
, find
C. 10
D.
and
D. 25
113. Is there enough information to prove the pair of triangles congruent? If so, state the postulate or theorem you
would use to prove that the triangles are congruent.
A. Not enough information
B. AAS
C. SAS
D. HL
114. Given the figure, SAC  ___________
C
Y
A
A)
A Y R
B)
Y R A
C)
RAY
D)
Y A R
R
S
115. What additional information is needed to prove PQR  PTR by the HL Theorem?
A)
Q  T
B)
QR  RT
C)
Q P R  T P R
D)
QP  TP
P
Q
R
T
116. Given the figure, which theorem or postulate proves the triangles congruent?
A)
ASA
B)
AAS
C)
SSS
D)
SAS
117. With the figure to the right, CSK  JKS and CS  JK . Complete the following congruency statement
and
provide the theorem why it which theorem or postulate that proves the triangles congruent?
SKC   __________ by __________
K
S
A)
C)
K S J b y S S S
J K S b y A S A
B)
D)
KSJ by SAS
C
J
J K S b y S A S
118. Given the figure, what postulate or theorem proves the right triangles congruent?
A)
HL
B)
LL
C)
HA
D)
LA
119. Given EDH  GFH , what additional information is needed
to prove DHE  FHG by the ASA postulate?
D
E
H
G
A)
G H H E
B)
DE  FG
C)
G E F D
D)
F H D H
120. What are the three undefined terms? _______________________________
F