GEOMETRY A
1.
Point, line, and plane
2.
1
3.
3
4.
1
5.
–3 and 13
6.
b  23, c  30
7.
30
8.
8
9.
20
10.
130
11.
12
12.
10
13.
25
14.
25
15a.
EG  FH
15b.
43
16.
55o
17.
30
18.
110o
19a.
5
19b.
30o
20.
x  20, y  80
21.
F  x, y    x,  y 
22.
F  x, y     x, y 
23.
F  x, y    y, x 
24.
F  x, y     x,  y 
25.
F  x, y    x  5, y  3
26.
C
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Semester Exam Review Answers
1
GEOMETRY A
Semester Exam Review Answers
y
27a.
27b.
B
A
D
C
x
27c.
C  3, 2 , C  3, 2 
27d.
P  x, y     x, y  4 The reflection across the y-axis makes the x-coordinate
the opposite, while the translation downward subtracts 4 from the ycoordinate.
28a.
warm blooded
dog
28b.
28c.
28d.
28e.
If an animal is warm-blooded, then the animal is a dog.
If an animal is not a dog, then the animal is not warm-blooded.
If an animal is not warm-blooded, then the animal is not a dog.
The contrapositive is true.
29a.
29b.
29c.
29d.
If I am a teenager, then I am between the ages of 13 and 19, inclusive.
If I am not between the ages of 13 and 19, inclusive, then I am not a teenager.
If I am not a teenager, then I am not between the ages of 13 and 19, inclusive.
The converse, inverse, and contrapositive are all true.
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GEOMETRY A
Semester Exam Review Answers
30a.
You can vote
You are 19 yrs old
30b.
If X represents a voter, then the X is inside the box. It may or may not be in the
oval, so the statement is not necessarily true.
31.
Chris will go to the game, and he will bring Jane.
32.
Triangle ABC is equiangular.
33.
Sally does not study for the test.
34.
C
35.
Inductive reasoning
36.
Deductive reasoning
37.
Deductive reasoning
38.
Inductive reasoning
39.
If it is sunny outside today, then I will go to the store
If I go to the store, then I will buy candy
If I buy candy, then I will not eat my dinner.
40.
If I listen carefully in class, then I will do my homework.
If I do my homework, then I will do well on my test.
If I do well on my test, then I will get a reward.
If I get a reward, then it will be a video game.
41a.
4
41b.
8
41c.
an infinite number
42.
43.
A
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GEOMETRY A
Semester Exam Review Answers
44.
Property
Parallelogram
Rectangle
Square
Rhombus
x
x
x
x
Opposite sides congruent
Only one pair of opposite sides
parallel
x
Opposite angles congruent
x
x
x
x
Each diagonal forms 2 congruent
triangles
x
x
x
x
Diagonals bisect each other
x
x
x
x
x
x
Diagonals congruent
Diagonals perpendicular
x
x
A diagonal bisects two angles
x
x
All angles are right angles
x
All sides are congruent
x
x
x
45.
85
46.
x  20, y  110
47a.
lines n and p. Corresponding angles are congruent.
47b.
lines l and m. Alternate interior angles are congruent.
47c.
lines l and m. Same side adjacent interior angles are supplementary.
48.
x  30, y  5
49.
A
50.
540o
51.
156o
52.
40o
53.
8
54.
6 sides
55.
4,5,6,7,8,9,10,11,12,13,14
56.
y  110
57.
36o
58.
x  6.5
59.
x  5.5, y  22
60.
x  20
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Trapezoid
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GEOMETRY A
61.
Semester Exam Review Answers
x  30
y
62.
A
x
B

D
C
The quadrilateral is a parallelogram.
The slopes of AB & CD equal 2, so AB CD .
The slopes of AD & BC equal –3, so AD BC .

63a.
The quadrilateral is not a rectangle or a square, since the slopes of AD & CD
are not opposite reciprocals (do not have a product of –1).
 The quadrilateral is not a rhombus since the slopes of the diagonals are not
1
opposite reciprocals. mBD  , m AC  7 .
3
3 parallelograms
63b.
 1, 1 , 3,3 , and  5, 1
64.
2
7
The triangle is a right triangle. m AB  , m AC   . So AB  AC .
7
2
65.
3.5,13
66a.
SAS
66b.
cannot be proven congruent
66c.
ASA
66d.
SSS
66e.
cannot be proven congruent
66f.
AAS
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GEOMETRY A
67.
A two-column proof is given. A paragraph or flowchart proof is also acceptable.
Statements
1. BD is the perp. bisector of AC
2. BEA and BEC are right angles
3. BEA  BEC
4. AE  EC
5. BE  BE
6. BEA  BEC
7. BAC  BCA
68.
Semester Exam Review Answers
Reasons
1. Given
2. Definition of perpendicular
3. All right angles are congruent
4. Definition of bisector
5. Reflexive Property of Congruence
6. SAS
7. CPCTC
A two-column proof is given. A paragraph or flowchart proof is also acceptable.
Statements
1. BD EG
2. BCF  CFG
3. BC  FG
4. CF  CF
5. BCF  GFC
6. CBF  CGF
Reasons
1. Given
2. If 2 lines are cut by a transversal,
alternate interior angles are congruent.
3. Given
4. Reflexive property of congruence
5. SAS
6. CPCTC
Alternative proof: Given that BD EG and BC  FG , then one pair of opposite
sides of quadrilateral BCFG is parallel and congruent. Therefore BCFG is a
parallelogram. Since opposite angles of a parallelogram are congruent, then
CBF  CGF.
69a.
parallelogram
69b. rhombus
69c.
rectangle
69d. none of the figures
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GEOMETRY A
Semester Exam Review Answers
70a.
C
E
A
B
D
Justification: Congruent circles were constructed with centers at points A and B. Since
radii of congruent circles are congruent, AC  BC  AD  BD ; therefore ACBD is a
rhombus. In the rhombus, the diagonals are perpendicular, therefore AB  CD . Since
ACBD is a parallelogram the diagonals bisect each other. Therefore AE  EB , so CD is
the perpendicular bisector of AB .
70b.
A
D
B
C
Justification: AB  BC since they are the radii of the same circle. AD  DC since they
are constructed using the same compass setting. BD  BD by the reflexive property of
congruence. Therefore ABD  CBD
by SSS. ABD  CBD by CPCTC, and by the definition of angle bisector
BD bisects ABC .
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GEOMETRY A
Semester Exam Review Answers
70c.
C
E
F
B
A
D
Justification: AB  CE , AD  CF since they were drawn by the same compass setting.
BD  EF since they were drawn with the same compass setting. Therefore
BAD  ECF by SSS. Therefore BAD  ECF by CPCTC. Finally by the converse
of the corresponding angles postulate, CF // AD .
70d.
B
A
D
C
Justification. I drew segments between A and B and B and C. I constructed the
perpendicular bisector of AB . Every point on that line is equidistant from points A and
B. I constructed the perpendicular bisector of BC . Every point on that line is equidistant
from points B and C. Therefore, point D, the intersection of those two perpendicular
bisectors, is equidistant from points A, B, and C.
71.
D
72.
B
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