Download Final Review Geometry A Fall Semester

Final Review Geometry A Fall Semester
Multiple Response
Identify one or more choices that best complete the statement or answer the question.
____
1. Which graph shows a triangle and its reflection image over the x-axis?
y
a.
c.
–4
4
4
2
2
–2
2
4
–2
–2
–2
–4
–4
b.
d.
y
–4
–4
x
4
2
2
2
4
–4
x
–2
–2
–2
–4
–4
Matching
Match each vocabulary term with its definition.
a. collinear
e.
b. segment
f.
c. line
g.
d. plane
h.
2
4
x
2
4
x
y
4
–2
y
point
ray
undefined term
coplanar
____
2. a basic figure that is not defined in terms of other figures
____
3. points that lie on the same line
____
4. a flat surface that has no thickness and extends forever
____
5. a straight path that has no thickness and extends forever
____
6. a location that has no size
____
7. points that lie in the same plane
Match each vocabulary term with its definition.
a. line
e.
b. opposite rays
f.
c. postulate
g.
d. ray
h.
plane
vertex
endpoint
segment
____
8. a point at an end of a segment or the starting point of a ray
____
9. a part of a line that starts at an endpoint and extends forever in one direction
____ 10. a statement that is accepted as true without proof, also called an axiom
____ 11. the common endpoint of the sides of an angle
____ 12. two rays that have a common endpoint and form a line
____ 13. a part of a line consisting of two endpoints and all points between them
Match each vocabulary term with its definition.
a. exterior of an angle
f.
b. interior of an angle
g.
c. vertical angles
h.
d. acute angle
i.
e. obtuse angle
right angle
straight angle
complementary angles
supplementary angles
____ 14. the nonadjacent angles formed by two intersecting lines
____ 15. an angle formed by two opposite rays that measures 180°
____ 16. an angle that measures greater than 0° and less than 90°
____ 17. an angle that measures 90°
____ 18. the set of all points between the sides of an angle
____ 19. an angle that measures greater than 90° and less than 180°
____ 20. the set of all points outside an angle
Match each vocabulary term with its definition.
a. congruent angles
e.
b. angle bisector
f.
c. vertical angles
g.
d. linear pair
h.
supplementary angles
exterior angles
adjacent angles
complementary angles
____ 21. two angles in the same plane with a common vertex and a common side, but no common interior points
____ 22. two angles whose measures have a sum of 90°
____ 23. two angles whose measures have a sum of 180°
____ 24. a ray that divides an angle into two congruent angles
____ 25. a pair of adjacent angles whose noncommon sides are opposite rays
____ 26. angles that have the same measure
Match each vocabulary term with its definition.
a. translation
e.
b. transformation
f.
c. rotation
g.
d. reflection
h.
position
dimension
image
preimage
____ 27. a shape that results from a transformation of a figure
____ 28. the original figure in a transformation
____ 29. a transformation across a line
____ 30. a change in the position, size, or shape of a figure
____ 31. a transformation about a point P, such that each point and its image are the same distance from P
____ 32. a transformation in which all the points of a figure move the same distance in the same direction
Match each vocabulary term with its definition.
a. acute triangle
e. isosceles triangle
b. equilateral triangle
f. equiangular triangle
c. right triangle
g. scalene triangle
d. obtuse triangle
____ 33. a triangle with three acute angles
____ 34. a triangle with at least two congruent sides
____ 35. a triangle with one obtuse angle
____ 36. a triangle with three congruent sides
____ 37. a triangle with one right angle
Match each vocabulary term with its definition.
a. interior angle
e. interior
b. complementary angles
f. remote interior angle
c. supplementary angles
g. exterior
d. exterior angle
____ 38. an angle formed by one side of a polygon and the extension of an adjacent side
____ 39. an angle formed by two sides of a polygon with a common vertex
____ 40. an interior angle of a polygon that is not adjacent to the exterior angle
____ 41. the set of all points outside a polygon
____ 42. the set of all points inside a polygon
Match each vocabulary term with its definition.
a.
b.
c.
d.
exterior angle
corresponding angles
interior angle
included angle
e. vertex angle
f. included side
g. corresponding sides
____ 43. angles in the same relative position in two different polygons that have the same number of angles
____ 44. the angle formed by the legs of a triangle
____ 45. the common side of two consecutive angles of a polygon
____ 46. sides in the same relative position in two different polygons that have the same number of sides
____ 47. the angle formed by two adjacent sides of a polygon
Match each vocabulary term with its definition.
a. isosceles triangle
e. triangle rigidity
b. base angle
f. base
c. scalene triangle
g. legs of an isosceles triangle
d. equiangular triangle
____ 48. a property of triangles that states that if the side lengths of a triangle are fixed, the triangle can have only one
shape
____ 49. a triangle with three congruent angles
____ 50. the side opposite the vertex angle of a triangle
____ 51. one of the two congruent sides of the isosceles triangle
____ 52. one of the two angles that have the base of the triangle as a side
Match each vocabulary term with its definition.
a. paragraph proof
e. congruent polygons
b. two-column proof
f. corollary
c. coordinate proof
g. CPCTC
d. auxiliary line
____ 53. a style of proof that uses coordinate geometry and algebra
____ 54. two polygons whose corresponding sides and angles are congruent
____ 55. a theorem whose proof follows directly from another theorem
____ 56. an abbreviation for “Corresponding Parts of Congruent Triangles are Congruent,” which can be used as a
justification in a proof after two triangles are proven congruent
____ 57. a line drawn in a figure to aid in a proof
Short Answer
58. Name the smallest angle of
The diagram is not to scale.
C
9
10
11
A
59. If
B
what is the relationship between
D
A
B
C
60. List the sides in order from shortest to longest. The diagram is not to scale.
J
33°
71°
K
76°
L
61. The vertices of a triangle are P(–8, 6), Q(1, –3), and R(–6, –3). Name the vertices of after a reflection over the
line y = x.
62. The vertices of a triangle are P(–3, 8), Q(–6, –4), and R(1, 1). Name the vertices of
63. Name three non collinear points.
.
P
N
G
R
64. Name a plane that contains
.
R
W
C
A
T
65. D is between C and E.
C
=
D
4x + 8
,
=
27
E
, and DE = 27. Find CE.
6x
66. K is the midpoint of
.
67. Find the measure of
and
. Find JK, KL, and JL.
. Then, classify the angle as acute, right, or obtuse.
C
D
B
O
68. m
and m
. Find m
A
.
I
L
K
J
69.
bisects
,m
70. Tell whether
and
, and m
. Find m
.
are only adjacent, adjacent and form a linear pair, or not adjacent.
F
1
B
A
2
3
4
G
C
71. Find the measure of the complement of
, where m
72. Name all pairs of vertical angles.
J
M
L
K
N
73. Find the coordinates of the midpoint of
with endpoints C(1, –6) and M(7, 5).
y
8
6
M
4
2
–8
–6
–4
–2
2
4
6
8
x
–2
–4
–6
C
–8
74. Find CD and EF. Then determine if
.
y
5
4
C
3
D
2
E
–5
–4
F
–3
–2
1
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
75. A figure has vertices at E(–3, 1), F(1, 1), and G(4, 5). After a transformation, the image of the figure has
vertices at E’(–3, –1), F’(1, –1), and G’(4, –5). Draw the preimage and image. Then identify the
transformation.
76. Find the coordinates for the image of
EFG after the translation (x, y)
(x – 6, y + 2). Draw the image.
y
7
E
–7
7
x
F
G
–7
77. Tell whether the transformation appears to be a reflection. Explain.
78. Tell whether the transformation appears to be a translation. Explain.
79. Rotate
80.
with vertices R(4, –1), S(5, 3), and Q(3, 1) by 90° counterclockwise about the origin.
has vertices A(3, 1), B(4, 5), and C(2, 3). Rotate
then reflect it across the x-axis.
90° counterclockwise about the origin and
81. Give an example of alternate interior angles, alternate exterior angles, same side interior angles and
corresponding angles.
3 4
2 1
7 8
6
5
82. Draw two lines and a transversal such that 1 and 2 are alternate interior angles, 2 and 3 are
corresponding angles, and 3 and 4 are alternate exterior angles. What type of angle pair is 1 and
83. Find .
A
xº
C
(3x - 70)º
B
84. Find m
.
R
>>
U
(4x – 24)º
T
S (3x)º
V
>>
85. Use the slope formula to determine the slope of the line containing points A(6, –7) and
B(9, –9).
4?
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
A
–8
B
–10
86. Write the equation of the line with slope 3 through the point (8,-1) in point-slope form.
87. Determine whether the pair of lines
88. Classify
and
are parallel, intersect, or coincide.
by its angle measures, given m
,m
, and m
.
D
30º
75º
60º
A
B
89.
C
is an isosceles triangle.
has length
.
=
and
=
. Find AB.
3 x+ 3
A
B
8 x- 5
6 x+ 3
C
90. Find
and
, given
,
, and
.
N
F
D
E
91. Find m
A
P
, given
,
B
E
D
C
92. Given that
M
, and m
.
F
and m
= 27 , find m
.
E
27º
A
D
C
B
93. Tom is wearing his favorite bow tie to the school dance. The bow tie is in the shape of two triangles.
Given:
,
,
,
Prove:
B
D
C
A
E
Complete the proof.
Proof:
1.
,
Statements
,
Reasons
1. Given
2.
3.
4.
5. [3]
2. Given
3. [1]
4. [2]
5. Definition of congruent triangles
4x
2x
-2
94. Find the value of x.
8
95. Find m
.
P
R
|
|
2xº
(x + 10)º
Q
96. Show that GHIJ is a parallelogram for x = 5 and y = 8.
5x-10
H
I
3y
G
5y-16
7x-20
J
97. TRSU is a rhombus. Find
R
2x + 5
5x + 2
T
U
.
S
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 98. Which three lengths CANNOT be the lengths of the sides of a triangle?
a. 23 m, 17 m, 14 m
c. 5 m, 7 m, 8 m
b. 11 m, 11 m, 12 m
d. 21 m, 6 m, 10 m
____ 99. Which three lengths could be the lengths of the sides of a triangle?
a. 12 cm, 5 cm, 17 cm
c. 9 cm, 22 cm, 11 cm
b. 10 cm, 15 cm, 24 cm
d. 21 cm, 7 cm, 6 cm
____ 100. Two sides of a triangle have lengths 6 and 17. Which expression describes the length of the third side?
a. at least 11 and less than 23
c. greater than 11 and at most 23
b. at least 11 and at most 23
d. greater than 11 and less than 23