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2012 Geometry Midterm Exam Review
Basic Geometry Vocabulary and Symbols (chapter 1):
1) For each statement, decide if it is true or false based on the picture. If the statement is false, correct it.
a) Points A, B, and H are collinear.
A
b) Point A lies on line m.
c) Points B, C, and H are coplanar.
B
C
D
d) Points E, J, and F are collinear.
H
e) Plane ABC and plane BCF intersect at point B.
E
2) Given: AB  2 x  10 ,
J
F
BC  5x  3 ; AC  28 , find x.



A
B
C
m
3) Given: AB  2x  3 , BC  8 ; AC  4x  3 , find x.

A

B

C
4) Let B be between C and D. Use the information below to solve for x.
CB  2 x  3
BD  x  1
CD  9x 10
5) Find the distance between the points 1, 3 and  3,5 . Answer in simple radical form.
6) Find the coordinates of the midpoint of a segment with endpoints 10, 7  and  14, 4 .
7) Find the other endpoint of the segment given endpoint A(1, 4) and midpoint B(2, 6) .
8) Find the length of KJ given endpoints K  2,1 and J 10, 4 .
l
9) A square with an area of 121in 2 has a perimeter of _______ inches.
M
10) NQ bisects MNP . Find the value of x.
MNQ  8 x  5
Q
N
PNQ  6 x  11
P
11) Find the measure of ACD .
A
13) What type of angle is BCD ? What type of angle is ACD ?
What type of angle is ACB ?
C
52
0
D
B
12) ACD and BCD are a _____________ pair.
13) 1 and 2 are supplementary angles. 1 and 3 are vertical angles. If the m2  54 , find
m3 .
14)
4 and 5 are complementary angles. If m4  52 , what is the m5 ?
15) Two angles form a linear pair. The measure of one angle is six more than twice the measure of the
other angle. Find the measure of each angle.
16) Solve for y in the diagram.
(10y – 35)
(y + 19)
Find the values of the variables for 17-19.
(2x – 5)
17) x =___________
(x – 25)
(10z + 5)
(5y)
18) y = __________
19) z = __________
Use the information below to solve questions 20-22.
D is in the interior of ABC.
mABD = (5x + 9)
mABC = (17x – 5)
mDBC = 70
20) x = ___
21) mABD = ________
22) mABC = ________
Logic (chapter 2):
Use the statements below to complete questions 23-24..
Statement p: You are in France.
Statement q: You are in Europe.
23) Write q  p
24) Write  p   q
Use the given conditional statement to complete questions 25-27.
If you study, then you will pass your exam.
25) What is the hypothesis?
26) Write the converse?
27) What is the inverse?
28)
Statement 1: If you practice, then you will be ready.
Statement 2: If you are not ready, then you did not practice.
Statement 2 is the _______________________ of statement 1.
29)
Statement 1: If an angle has a measure of 90, then it is a right angle.
Statement 2: If an angle does not have a measure of 90, then it is a not a right angle.
Statement 2 is the _______________________ of statement 1.
30)
Write a biconditional statement given the following:
Statement 1: If two angles are supplementary, then their sum is 180.
Statement 2: If the sum of two angles is 180, then they are supplementary.
31)
Is the statement valid? If it is, state the law that makes it valid.
a) Given: If it is snowing, then there will be no school.
There is no school.
Conclusion: It is snowing.
b) Given: If you like music, then you like to dance.
If you like to dance, then you can do the robot dance.
Conclusion: If you like music, then you can do the robot dance.
c) Given: If you are in law school, then you study a lot.
Todd is in law school.
Conclusion: Todd studies a lot.
32) Fill in the missing reasons.
4(x – 2) = 10 + x
Statements
1. 4(x – 2) = 10 + x
2. 4x – 8 = 10 + x
3. 3x – 8 = 10
4. 3x = 18
5. x = 6
Reasons
1.
2.
3.
4.
5.
Name the property that justifies each statement for questions 33-35.
33) If AB  BC , then BC  AB
34) If XY  YZ and YZ  ZA then XY  ZA .
35) CD  CD
36) If two planes intersect, then their intersection is a ______________________.
37) Between any two points there exists exactly one ______________________.
38) In a plane, if two lines are ____________ to the same line, then they are ___________ to each
other.
Use the correct quantifier “all,” “some,” or “no,” or to complete the statement.
39)
______ polygons are triangles.
40)
______ squares are quadrilaterals.
41)
______ quadrilaterals are triangles.
42)
______ quadrilaterals are squares.
Polygons
quadrilaterals
triangles
squares
Parallel and Perpendicular Lines (chapter 3):
For problems 43-48, use the figure to the right.
43) Which angles are consecutive interior angles?
44) Which angles are corresponding angles?
45) What type of angles are 3 and 6 ?
1 2
Given: a // b
3 4
a
5 86
7 8
b
46) What type of angles are 2 and 7 ?
47) If m6  125 , then the m4  _____
48) If m2  120 , then the m5  _____
49) Which value of x would make lines x and y parallel?
x
100
y
(3x + 46)
For questions 50-52, decide if the lines are parallel. Circle YES or NO
50)
YES
NO
51) YES
NO
52) YES
NO
130
140
120
120
140
50
53) Find the slope of the line that passes through (4, 1 ) and (4, 7).
54) Find the slope of the line that passes through (-3, 2 ) and (9, -1).
55) Write the equation of the line in slope-intercept form with slope of 3/4 and passing
through ( -16, 7 ).
56) Write the equation of the line in slope-intercept form that is parallel to 3x+4y = 10 and passing
through ( 4, -9 ).
57) Write the equation of the line in slope-intercept form that is perpendicular to y = -3x-11 and passing
through ( 24, 1 ).
Triangle Congruence (chapter 4):
58) Find x.
56
x
59) a) What is the value of x?
b) Classify the triangle according to its sides and also its angles.
(3x)
60) a) What are the values of x and y?
b) Classify the triangle according to its angle and according to its sides.
x
48
(2 y )
61) A triangle with side lengths 7 cm, 4 cm, and 5 cm is classified as a(n) _________ triangle.
Solve each problem for the value of the unknown(s) for questions 66-70.
62) x = ________
(3x)
63) y = _______
(y – 7)
(6x + 18)
125
(4y + 12)
64) n = ________
65) x = _______
(4x)
5n - 8
3n + 2


(5x + 20)
5n - 10
(7x)
66) x = _________
(3 x  3)
Decide if the two triangles can be proved congruent. If so, name the postulate(s) or
theorem(s) that justifies the congruence. If not, write none.
67) _________
68) _________
69) ________
70) ________
71) ________
72) _________
73) What is the third congruency needed to prove the  MNQ   PNO by AAS?
M
O
N
Q
P
74) If  ABC   XYZ, list the six congruency statements of these triangle’s corresponding parts.
a)___________________
d)___________________
b)___________________
e)___________________
c)___________________
f)____________________
75) State the congruence that is needed to prove
A
D
B
E
C
ABC  DEF using the given postulate or theorem.
F
a) Given: BC  EF ; use Hypotenuse-Leg Congruence Theorem. ______________
b) Given: AB  DE , AC  DF ; use the SSS Congruence Postulate_____________
c) Given: A  D, B  E ; use the AAS Congruence Theorem______________
d) Given: A  D, C  F ; use the ASA Congruence Postulate._____________
Properties within Triangles (chapter 5):
76) List the sides of CDE from shortest to longest.
C
60
50
D
E
77) List the angles of RAT from largest to smallest.
R
14
16
T
15
A
For questions 78-81 decide if the following segment lengths are possible sides of a triangle?
Answer YES or NO.
78)
20, 14, 15
79) 2, 6, 10
80) 2, 4, 5
81) 4, 4, 8
82) A triangle has one side of length 10 and another side of length 6. Describe the possible lengths of the
third side.
83) Describe the length of x with an inequality statement.
12
30
11
80
x
12
B
84) What can you conclude about the location of point D in the figure?
11
A
C
15
15
D
85) Identify the special line ED in CAT.
T
D
A
E
C
86) Find the perimeter of RAT _________
R
87) Find the length of AR ______________
S
U
88) Find the length of UT _______________
A
89) Find the perimeter of SUN_____________
5x  5
5
6
N
2x  4
19
Q
R
90) WY is the midsegment of QRS . Find the value of x.
3
2x  8
W
B
91) What is the length of XY ?____________
10
Y
X
92) m YWC = ______________
9
10
93) XY // ____
40
8
A
94) Find the perimeter of XYW
95) k = ______
96) y = ______
14
9
D
12
97) AX = __________
B
y
V
X
8
W
Given that V is the centroid of ABC, answer questions 95-97.
A
G
k
Y
S
9
C
T
C
Name the point of concurrency shown by the sketch for questions 98-100. Describe the
special relationships/properties of the point and related segments
98)
99)
100)
101). The circumcenter of a right triangle is
Always
Sometimes Never
inside the triangle.
102) The incenter of an acute triangle is
Always
Sometimes Never
inside the triangle.
103) The centroid of an obtuse triangle is
Always
Sometimes Never
outside the triangle.
104) The incenter of a right triangle is
Always
Sometimes Never
on the hypotenuse.
Write a two-column proof .
105) Given: EN bisects  KEV
EN  KV
Prove:
KN  NV
E
K
N
V
Write a two-column proof .
B
106) Given: AB // CD
DC  BA
Prove:
3
A
4
1 2
AD // BC
C
D
Similarity (chapter 6):
In the diagram, ABCDE
FGHJK .
4
107) Find the scale factor.
A
B
K
10
F
8
C
108) Find the value of x.
x
12
109) Find the perimeter of ABCDE .
G
8
E
D
J
10
H
Determine whether the triangles are similar. If so, write a similarity statement and the postulate or theorem that
justifies your answer.
110)
B
111)
C
A
35
D
E
Find the length of AB .
112)
113)
114) The area of a rectangle is 64 in2. The ratio of the length to the width is 4:1. Find the length and width.