Download 1 Part I Answer all 20 questions in this part on the

Part I
Answer all 20 questions in this part on the answer sheet provided. Each correct answer
will receive 2 credits. No partial credit will be allowed. For each question, write on the
separate answer sheet the numeral preceding the word or expression that best completes the
statement or answers the question. [20]
1 Which of the following is logically equivalent to the statement:
“Access is denied if the password is incorrect.”
(1) “If the password is correct, then access is granted.”
(2) “If access is denied, then the password is correct.”
(3) “If the password is incorrect, then access is granted.”
(4) “If access is granted, then the password is correct.”
2 Two angles are both vertical and supplementary. Which conclusion is true?
(1) Each angle has a measure of 45 .
(2) Each angle is congruent to an adjacent angle.
(3) Each angle is obtuse.
(4) Each angle is adjacent to an obtuse angle.
3 If PQRS is a parallelogram, which statement must be true?
(1) PR  QS
(3) P  S
(2) PS  QR
(4) P is supplementary to R
4 Which law of logic is correctly stated below?
[( p  q )  ~ p ]  q
(1) The Law of Modus Ponens
(3) The Law of Disjunctive Inference
(2) The Law of Modus Tollens
(4) The Law of the Contrapositive
Geometry RSH Midterm 2013 - 2014
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Use this space for
computations.
Use this space for
computations.
5 Which of the following could be used to prove that l // m?
l
a
c
m
e
g
b
d
f
h
(1) a  h
(3) a  d
(2) d  f
(4) b is supplementary to g
6 Given: AOD , OB bisects AOC ,
mAOC is 2 less than 6 times mCOD .
What is mBOC ?
B
A
C
O
D
(1) 26 degrees
(3) 154 degrees
(2) 13 degrees
(4) 77 degrees
7 Given: AD  AB , 1   2 .
Which additional information would you need to
prove that ADC  ADE by AAS  AAS ?
(1) C  E
(3) CD  ED
(2) CAD  EAD
(4) AC  AE
C
1
2
A
Geometry RSH Midterm 2013 - 2014
2
E
D
B
Use this space for
computations.
8 In the following diagram, D E F G H and I are all midpoints.
If the perimeter of GHI is 8 feet, what is the perimeter of ABC ?
A
I
E
D
H
G
B
C
F
(1) 32 feet
(3) 4 feet
(2) 16 feet
(4) 64 feet
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9 Which of the following is true regarding the circumcenter of a triangle?
(1) It is equidistant from the three sides of the triangle.
(2) It is the point of concurrency of the three altitudes of the triangle.
(3) It is located on the hypotenuse of a right triangle.
(4) It is located on the vertex of the right angle of a right triangle.
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11 The lines 3 y  1  6 x  4 and 2 y  1  x  9 are
(1) parallel
(2) perpendicular
(3) the same line
(4) neither parallel nor perpendicular
Geometry RSH Midterm 2013 - 2014
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12 In the diagram below of PRT, Q is a point on PR, S is a point on TR, QS is drawn, and
RPT  RSQ.
Which reason justifies the conclusion that PRT ~ SRQ ?
(1) AA
(3) SAS
(2) ASA
(4) SSS
13 In ABC, m<A = 70, m<B = 65, and m<C = 45. Which expression correctly relates the lengths
of the sides of this triangle?
(1) AB < BC < CA
(3) AC < BC < AB
(2) AB < AC < BC
(4) BC < AC < AB
14 In the diagram of ABC below, Jose found centroid P by constructing the three medians. He measured
CF and found it to be 6 inches.
If PF  x , which equation can be used to find x?
(1) x  x  6
(3) 3x  2 x  6
(2) 2 x  x  6
(4) x 
Geometry RSH Midterm 2013 - 2014
2
x6
3
4
15 In ABC, point D is on AB, and point E is on BC such that DE AC. If DB  2, DA  7,
and DE  3, what is the length of AC ?
(1) 8
(3) 10.5
(2) 9
(4) 13.5
16 Which set of numbers represents the lengths of the sides of a triangle?
(1) {5, 18, 13}
(3) {16, 24, 7}
(2) {6, 17, 22}
(4) {26, 8, 15}
17 The statement "Maya plays on the basketball team or Maya joins the ski club" is false. Which
statement is true?
(1) Maya plays on the basketball team and Maya joins the ski club.
(2) Maya plays on the basketball team and Maya does not join the ski club.
(3) Maya does not play on the basketball team and Maya joins the ski club.
(4) Maya does not play on the basketball team and Maya does not join the ski club.
18 Square ABCD has diagonals AC and BD . If AC = 5x + 13 and
BD  11x  5 , what is the value of AB?
1) 28√2
2) 56√2
3) 14√2
4) 14
19 In which type of triangle do the 3 altitudes intersect outside of the triangle?
1) right
2) acute
3) obtuse
4) equilateral
20
1) 9
2) 6
Geometry RSH Midterm 2013 - 2014
3) 5
4) 8
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Part II
Answer all questions in this part. Each correct answer will receive 5 credits (unless noted
otherwise). Clearly indicate all necessary steps, including appropriate formula substitutions,
diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with
no work shown will receive only 1 credit. [35]
21 Use a truth table and the symbolic form to prove the law of Modus Tollens
22 In each case, do one of the following:
(4 pts)
1) Give a valid conclusion and state the law of logic used.
2) State “no conclusion possible”.
pq
~p
a]


b]
a ~ b
~ a ~ b
b
~a

c]

Geometry RSH Midterm 2013 - 2014


6
~vw
~v
d]


23 Two sides of a triangle have lengths 17 and 5. What is the range of values for the third side?
24 Find the measure of each exterior angle of a regular convex polygon if the sum of its interior
angles is 4,140 degrees.
25
Geometry RSH Midterm 2013 - 2014
(6 pts)
7
26 Determine the value of x (in simplest radical form, if necessary):
3 6
2
x
60
90
90 45
27 Find the value of x in the diagram below:
x
x–6
Geometry RSH Midterm 2013 - 2014
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8
Part III
Answer all questions in this part. Each correct answer will receive 8 credits. Clearly indicate
all necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.
[24]
28
(use of graph paper not necessary and optional)
Geometry RSH Midterm 2013 - 2014
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29 Please complete the following proof using the statements/reasons format:
B
A
D
C
Given: BD bisects ABC
ABC is not isosceles
Prove: BD is not an altitude.
Geometry RSH Midterm 2013 - 2014
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30 Please complete the following proof using the statements/reasons format:
Given:
B
AB  AD
CB  CD
Prove:
A
E
C
D
Geometry RSH Midterm 2013 - 2014
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EC bisects BED