Intel-Assess CST Mirrors

Intel-Assess CST Mirrors
Geometry: Math CST Mirror
Copyright © 2011 Intel-Assess, Inc.
Geometry: Math CST Mirror
Section 1
Directions: Answer all questions on the answer sheet provided. When you are finished with a page,
go on to the next page.
Read questions 1 through 33 and select the best answer.
1
In the diagram below, ∠ A is a right
angle, AB = 14 , and BC = 28 .
3
What is the measure of ∠ B ?
2
A.
75˚
B.
30˚
C.
60˚
D.
45˚
Which of the following defines the
cosine for an acute angle of a right
triangle?
A.
the length of the leg opposite to the
angle divided by the length of the
hypotenuse
B.
the length of the leg adjacent to the
angle divided by the length of the
leg opposite to the angle
C.
the length of the leg opposite to the
angle divided by the length of the
leg adjacent to the angle
D.
the length of the leg adjacent to the
angle divided by the length of the
hypotenuse
What is the distance from the point
(6, 2) to the point (1, − 1) ?
A.
50
B.
34
C.
48
D.
16
—1—
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Geometry: Math CST Mirror
4
A student wrote the following
statement.
5
Every parallelogram is a rhombus.
A farmer built a fence around his
house. The house is 150 feet by 100
feet. The fence is 50 feet away from
the house on all sides, as shown.
Which figure is a counterexample to
prove this statement false?
A.
B.
C.
What is the perimeter of the fence?
D.
6
A.
600 feet
B.
700 feet
C.
900 feet
D.
450 feet
What is the area of a rhombus with
diagonals that measure 4 cm and 6
cm?
A.
24 cm2
B.
6 cm2
C.
12 cm2
D.
48 cm2
—2—
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Geometry: Math CST Mirror
7
Quadrilateral ABCD is inscribed in
¯ is a
circle O below. Segment AC
diameter of the circle.
8
Read the assertion in the box.
If a diagonal is drawn on a
quadrilateral such that it forms two
right triangles, then the
quadrilateral is a rectangle.
Which of the following is a
COUNTEREXAMPLE of this assertion?
A.
B.
What is the sum of the degree
measures of ∠ ABC and ∠ CDA ?
A.
90°
B.
180°
C.
270°
D.
360°
C.
D.
—3—
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Geometry: Math CST Mirror
11
9
What is m ∡ 1 in the quadrilateral
shown below?
What is the value of x?
10
A.
4.4
B.
8.5
C.
0.3
D.
7.9
In the diagram below, parallel lines l
and m are cut by a transversal. What
is the value of x?
12
A.
x = 60
B.
x = 30
C.
x = 70
D.
x = 50
13
A.
64∘
B.
28∘
C.
33∘
D.
57∘
What is the midpoint of a line
segment with the end points (2,4)
and (-2,2)?
A.
(0,3)
B.
(2,3)
C.
(2,1)
D.
(0,1)
Which of the following terms is
UNDEFINED in geometry?
A.
polygon
B.
point
C.
property
D.
postulate
—4—
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Geometry: Math CST Mirror
14
The figure below shows a square
pyramid on top of a cube.
15
Use the figure and table below to
answer the question.
What is the combined volume of the
pyramid and the cube?
A.
17,600 in.3
B.
9,600 in.3
C.
8,000 in.3
D.
11,200 in.3
Which of the following is BEST used
in the proof as the reason for step 5?
A.
the reflexive property
B.
the base angles of isosceles triangles
are congruent
C.
the corresponding parts of congruent
triangles are congruent
D.
the identity property
—5—
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Geometry: Math CST Mirror
16
The coordinate plane below shows
the location of polygon STUVW .
17
Which of the following pictures
shows the construction of an angle
bisector?
A.
B.
C.
The polygon will be translated using
this rule.
(x, y) → (x − 2, y − 6)
How many vertices of the translated
image will be located in quadrant III?
A.
0 vertices
B.
3 vertices
C.
2 vertices
D.
1 vertex
D.
—6—
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Geometry: Math CST Mirror
18
Study the diagram and the twocolumn proof for the Vertical Angles
Theorem.
19
Which of the following is the missing
statement for line 3?
A.
m ∠ 1 + m ∠ 3 = 180°
B.
m ∠1=m ∠3
C.
m ∠1+m ∠2=m ∠2+m ∠3
D.
m ∠2=m ∠2
20
Given parallelogram ABDC, what are
the coordinates of point D?
A.
(a, b)
B.
(a + b, c)
C.
(a + c, b)
D.
(b, c)
A solid cylinder has a radius, r, and a
height, h. What is the surface area
of the cylinder?
A.
2πr 2 + 2πr 2h
B.
2πr 2 + 2πrh
C.
πr 2 + 2πrh
D.
2πrh
—7—
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Geometry: Math CST Mirror
21
22
A circular dinner plate has a
diameter of 10 inches. A circular
dessert plate has a diameter of 7
inches. What is the ratio of the area
of the dinner plate to the area of the
dessert plate?
23
Triangle EFG is an obtuse triangle.
Pedro wants to prove by
contradiction that ΔEFG is NOT
equilateral. Which of these
statements should Pedro use to start
his proof?
A.
20:14
A.
ΔEFG is NOT equilateral.
B.
10:7
B.
ΔEFG is equilateral.
C.
100:7
C.
ΔEFG is NOT obtuse.
D.
100:49
D.
ΔEFG is obtuse.
What theorem or postulate can be
used to prove △ ABD ≅ △ CBD ?
A.
AAS
B.
Hypotenuse-Leg
C.
ASA
D.
SAS
24
Quadrilateral ABCD is a rectangle.
What is the value of x?
A.
2
B.
–1
C.
1
D.
3
—8—
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Geometry: Math CST Mirror
25
The diagram below shows ΔABC .
26
The diagram below shows a line
tangent to a circle at point A. The
measure of arc AB is 110°.
What inequality represents all
possible values of x?
A.
6<x
B.
-5 < x
What is the measure of angle x?
C.
1<x<6
A.
55°
D.
1
2
B.
35°
C.
70°
D.
125°
<x<
7
2
27
The figure below was drawn using a
straightedge and a compass. Both
arcs were drawn using the same
compass setting.
Using only this diagram and a
straightedge, a student can
construct which of the following?
A.
a bisected line segment
B.
concentric circles
C.
congruent angles
D.
parallel line segments
—9—
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Geometry: Math CST Mirror
28
The diagram shows a regular
→
→
octagon with AD and BC intersecting
at point X.
29
What is the measure of ∠ AXC?
A.
45°
B.
135°
C.
22.5°
D.
60°
Given the right triangle ABC, what is
the value of sin(A) in simplified
radical form?
A.
15
5
B.
3 6
C.
3
5
D.
— 10 —
Copyright © 2011 Intel-Assess, Inc.
6
2
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Geometry: Math CST Mirror
30
A contractor is going to set white,
triangle-shaped tiles and black,
diamond-shaped tiles on a
rectangular kitchen floor in the
pattern shown in the diagram.
31
The cube below has an edge length
of 8 cm. What is the length of
¯?
diagonal AB
A.
16 cm
The floor has an area of 5040 in2.
How many BLACK tiles does the
contractor need?
B.
83 cm
C.
8 2 cm
A.
420 black tiles
D.
8 3 cm
B.
280 black tiles
C.
1680 black tiles
D.
840 black tiles
32
The figure below shows a rectangle
inscribed in a circle. The rectangle is
8 centimeters tall and 6 centimeters
wide.
What is the circumference of the
circle?
A.
14π cm
B.
10π cm
C.
8π cm
D.
7π cm
— 11 —
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Geometry: Math CST Mirror
33
What is the area of this rectangle?
A.
24 ft2
B.
20 ft2
C.
10 ft2
D.
12 ft2
— 12 —
Copyright © 2011 Intel-Assess, Inc.
End of Section 1
Geometry: Math CST Mirror
Section 2
Directions: Answer all questions on the answer sheet provided. When you are finished with a page,
go on to the next page.
Read questions 34 through 65 and select the best answer.
34
On the coordinate plane below, ∆PQR
will be rotated 90˚ counterclockwise
about the origin to form ∆P'Q'R'.
35
36
Given △ ABC ≅ △ DEF , which of
these statements is also true?
A.
¯ ≅ EF
¯
AB
B.
The triangles are acute.
C.
The triangles are equilateral.
D.
¯ ≅ DE
¯
AB
A pyramid is shown below.
After the rotation, what will the
coordinates of point Q' be?
A.
(4,–5)
What is the volume of the pyramid?
B.
(–4,5)
A.
79 cm3
C.
(–5,4)
B.
1404 cm3
D.
(–5,–4)
C.
702 cm3
D.
468 cm3
— 13 —
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Geometry: Math CST Mirror
37
38
Which of the following is NOT always
true about a parallelogram?
A.
Both pairs of opposite angles are
congruent.
B.
The diagonals are perpendicular.
C.
Both pairs of opposite sides are
parallel.
D.
Opposite sides have the same
measure.
39
The figure below is composed of a
square and a triangle.
40
Which theorem or postulate can be
used to prove these two triangles
are congruent?
A.
ASA
B.
HL
C.
SSS
D.
SAS
In the figure below, isosceles △ ABC
is inscribed in the circle.
What is the area of the figure?
A.
352 mm2
B.
224
mm2
C.
448 mm2
A.
55°
D.
480 mm2
B.
260°
C.
220°
D.
110°
The measure of ∠ BAC is 40°. What
is the measure of arc ABC?
— 14 —
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Geometry: Math CST Mirror
41
A secant and a tangent are drawn
from point A to circle O, as shown
below.
42
Which of the following best
represents the construction of a
perpendicular bisector?
A.
B.
What is the value of x?
A.
10 3
3
B.
25
C.
5
2
D.
5
C.
D.
43
A certain regular polygon has two
diagonals from each vertex. What is
the measure of each exterior angle
of that polygon?
A.
72 °
B.
90 °
C.
108 °
D.
180 °
— 15 —
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Geometry: Math CST Mirror
44
In the diagram shown below, the
following are true.
45
A trapezoid is shown below.
AB = 100
DF = 5x + 10
DE = 7x − 27
∠A≅ ∠D
∠B≅ ∠F
¯ ≅ EF
¯
CB
What is the degree measure of angle
4?
What is the value of x?
A.
22
B.
18
C.
127
7
D.
37
2
A.
50°
B.
110°
C.
40°
D.
70°
— 16 —
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Geometry: Math CST Mirror
47
46
What is the measure of the
EXTERIOR angle of a regular
dodecagon?
The straightedge-and-compass
construction described below was
performed on ΔRST , shown above.
1.
2.
3.
Draw two intersecting circles with
the same radius using centers at
points S and T.
The circles intersect in two points,
↔
X and Y. Draw line XY .
↔
¯ at point P.
XY intersects side ST
¯
Draw segment RP .
Which of the following best names
¯ to
the relationship of segment RP
ΔRST ?
A.
median
B.
altitude
C.
angle bisector
D.
perpendicular bisector
A.
120°
B.
15°
C.
30°
D.
36°
— 17 —
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Geometry: Math CST Mirror
48
Circle C is shown below. In the circle,
m ∠ BCD = 18 ° .
49
What is the perimeter of the right
triangle pictured below?
What is the measure of MAJOR arc
BD?
A.
342°
B.
18°
C.
351°
D.
9°
A.
45 cm
B.
20 cm
C.
30 cm
D.
12 cm
— 18 —
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Geometry: Math CST Mirror
50
The diagram below shows a portion
of a metal beam.
51
Given trapezoid ABCD, where is D'
after a reflection in the line y = x?
In the diagram, BCDE and EGAB are
congruent isosceles trapezoids.
What is the area of each of those
trapezoids?
A.
(-2,4)
A.
11 square feet
B.
(2,4)
B.
12 square feet
C.
(-4,2)
C.
15 square feet
D.
(-2,-4)
D.
24 square feet
— 19 —
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Geometry: Math CST Mirror
52
Marla needs to replace a broken
piece of stained glass. The piece of
glass is shaped like a right triangle,
as shown below.
53
Based on the information given in
the diagram, which theorem or
postulate can be used to prove
ΔABC ∼ ΔADE ?
Which of the following can be used
to determine the length, in inches,
of side MP?
A.
tan 30 =
20
MP
B.
cos 30 =
20
MP
C.
cos 30 =
MP
20
tan 30 =
MP
20
D.
The figure below shows triangles
ABC and ADE.
A.
AA
B.
ASA
C.
SAS
D.
SSS
— 20 —
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Geometry: Math CST Mirror
54
A surveyor stands 58 feet from the
base of a tree and observes that the
angle of elevation from the ground
to the top of the tree is 36°.
55
What is the height of the tree?
Round your answer to the nearest
tenth.
A.
42.2 ft.
B.
46.9 ft.
C.
34.1 ft.
D.
79.8 ft.
56
What theorem or postulate can be
used to prove △ ABC ≅ △ ADC .
A.
Hypotenuse-Leg
B.
ASA
C.
SSS
D.
SAS
Which two triangles MUST be similar
triangles?
A.
two isosceles triangles, each with
two legs that are twice the length of
its base
B.
two scalene triangles, each with its
longest leg twice the length of its
shortest leg
C.
two acute triangles, each with its
longest leg twice the length of its
shortest leg
D.
two obtuse triangles, each with its
longest leg twice the length of its
shortest leg
— 21 —
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Geometry: Math CST Mirror
57
The diagram below shows a gate.
The brace for the gate is 6 feet long.
59
The figure below shows exterior
angles A, B, and C of a triangle. In
the figure, m ∠ A = 120∘ and
m ∠ C = 130∘ .
What is the approximate height of
the gate (x)?
58
A.
4.0 ft
B.
4.4 ft
C.
5.4 ft
D.
6.7 ft
What is m ∠ B ?
In right triangle ABC, angle C is the
3
right angle and tan(B)= 4 . What is
cos(A)?
A.
3
5
B.
4
3
C.
1
4
D.
4
5
A.
130°
B.
110°
C.
125°
D.
70°
— 22 —
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Geometry: Math CST Mirror
60
Two parallel lines are cut by a
transversal, as shown below.
61
The figure below shows two
tangents drawn from point D to
circle O.
Which angles are congruent?
A.
∠ 5 ≅ ∠ 7 and ∠ 6 ≅ ∠ 8
B.
∠ 1 ≅ ∠ 4 and ∠ 2 ≅ ∠ 7
C.
∠ 2 ≅ ∠ 4 and ∠ 3 ≅ ∠ 7
A.
16
D.
∠ 3 ≅ ∠ 5 and ∠ 6 ≅ ∠ 7
B.
12
C.
10
D.
14
¯?
What is the unit length of OD
62
Which of the following is NOT an
axiom of geometry?
A.
Any line segment can be extended
indefinitely in a line.
B.
Any two points can be joined by a
line.
C.
Any two right angles are congruent.
D.
Any two circles can be joined to
make a sphere.
— 23 —
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Geometry: Math CST Mirror
63
64
Which theorem or postulate can be
used to prove ΔABD ≅ ΔCBD given
¯?
that point D lies on AC
A.
Hypotenuse-Leg Theorem
B.
AA Postulate
C.
CPCTC
D.
SSA Postulate
65
A trapezoid has an altitude of 8 cm
and an area of 88 cm2. What is the
SUM of the measures of its bases?
A.
5.5 cm
B.
22 cm
C.
11 cm
D.
30 cm
What is the perimeter of the triangle
with a circle inscribed in it?
A.
77 units
B.
72 units
C.
73 units
D.
82 units
— 24 —
Copyright © 2011 Intel-Assess, Inc.

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