Transcript 2005 Geometry Released Test

GEOMETRY
Spring 2005
Released Test
1.
1.
2.
3.
4.
The measures of some angles are given
in the figure.
What is the value of x?
65
70
80
85
2. The figure shows line l intersecting lines r
and s. In the figure, ∠1 and ∠2 are 1. Alternate
interior angles
2. Alternate
exterior angles
3. Corresponding
angles
4. Consecutive
interior angles
3. The Department of Transportation wants to extend the
intersecting road across the highway, as indicated by the
dotted line. What should x be to ensure that the intersecting
road and the new construction form a straight line?
1.
2.
3.
4.
35 °
55°
105°
125°
4. The polygon shown is convex.
The sum of its interior angle measure is 1.
2.
3.
4.
900°
1,260°
1,620°
2,520°
5.Which statement would be sufficient to
prove that line l is parallel to line m?
1.
2.
3.
4.
AC ⊥ m
AB ⊥ l
AC ⊥ l
AB ⊥ AC
6. In this diagram, line d cuts three lines to
form the angles shown.
Which two lines are parallel?
1.
2.
3.
4.
a and b
a and c
b and c
No lines
are parallel
7. Quadrilateral QRST is placed on a coordinate
grid as shown. What coordinates for S make
QRST a parallelogram?
1.
2.
3.
4.
(8,6)
(8,10)
(12,6)
(12,10)
8. Which condition will guarantee
that line l parallel to line m?
1.
2.
3.
4.
∠1 ≅ ∠3
∠1 ≅ ∠6
∠6 ≅ ∠5
∠3 ≅ ∠5
9. The drawing shows a compass
and straightedge construction of 1.
2.
3.
4.
A perpendicular
to given line from
a point not on the
line
A perpendicular
to a given line at
a point on the
line
The bisector of a
given angle
An angle
congruent to a
given angle
10. Which point would be on a line
perpendicular to l through T?
1.
2.
3.
4.
W
X
Y
Z
11. To which point should a line segment
from A be drawn so that the resulting figure
is a rectangle?
1.
2.
3.
4.
W
X
Y
Z
12. XYZ is similar to STR. XY 6 and ST = 12.
If the perimeter of STR is 38, then what is the
perimeter of XYZ?
1.
2.
3.
4.
19
38
52
76
13. Let p represent √11 = z, and let q represent z is a
rational number. Which is a representation of the statement
below? If √11 = z, than z is not a rational number.
1.
2.
3.
4.
p→q
~p → ~q
p → ~q
~q → ~p
14. According to the Venn diagram,
which statement is true?
1.
2.
3.
4.
All isosceles
triangles are also
equilateral triangles.
All equilateral
triangles are also
isosceles triangles.
Some equilateral
triangles are also
isosceles triangles.
No isosceles
triangles are
equilateral triangles.
15. Which of the following statements
represents a valid argument?
1. If a > b and a > c,
than b > c.
2. If a> b and b > c,
then a > c.
3. If a < b and a < c,
then c < b.
4. If a > b and a > c,
then a > b + c.
16. Given: ∠AXY ≅ ∠ABC
∠AYX ≅ ∠ACB
Which is a true proportion?
1. AX/AB = AY/AC
= XY/BC
2. AX/XB = AY/YC
= XY/BC
3. XB/AX = YC/AY
= BC/XY
4. AX/AB = AC/AY
= XY/BC
17.
1.
2.
3.
4.
Given: AD and BC intersect at X
AX = XB
CX = XD
Which congruency statement is true?
∠ACX ≅ ∠BXD
∠ACX ≅ ∠DXB
∠ACX ≅ ∠BDX
∠ACX ≅ ∠DBX
18. Which list could not be the measures of
lengths of the three sides of a given
triangle?
1. 5 cm, 12cm,
15 cm
2. 2 ft, 6ft, 5 ft
3. 11 mi, 4 mi,
12 mi
4. 12 yd, 35 yd,
20 yd
19. In the drawing of triangle XYZ,
which angle has the least measure?
1. All angles have
the same
measure.
2. ∠XYZ
3. ∠ZXY
4. ∠XZY
20. If m∠A 65°, m∠B15°, m∠C100°, which list
order from shortest to longest?
1.
2.
3.
4.
AC, AB, BC
BA, BC, AC
BA, AC, BC
AC, BC, BA
21. A windlass is used to pull a boat to the dock. The rope
is attached to the boat at a point 7 feet below the level of
the windlass. What is the distance from the boat to the
dock when the rope is 25 feet?
1.
2.
3.
4.
25 ft
24 ft
18 ft
7 ft
22. The parallelogram has the measurements shown.
Which is closest to the length of the altitude, h?
1.
2.
3.
4.
19.63
8.91
8.67
6.81
23. For the triangle represented by the drawing,
which is the length of XY?
1.
2.
3.
4.
7.5 √2
7.5 √3
15√2
15√3
24. In rectangle ABCD, which of the following pairs
of segments are not necessarily congruent?
1.
2.
3.
4.
BD and AC
AB and CD
BC and DC
BE and CE
25. The town plaza in a certain town is a parallelogram. The town’s
planning committee has decided to build a fountain at the center of the
plaza. This sketch shows the corner points when placed on a coordinate
grid. Which coordinates show where the fountain will be located
1.
2.
3.
4.
(2, 0.50
(O.5, 2)
(3, 1.5)
(1.5, 1)
26. Quadrilateral ABCD is parallelogram.
Which of the following must be true?
1.
2.
3.
4.
AB = AD
AC = BD
∠A ≅ ∠D
∠B ≅ ∠D
27. ABCD is a rhombus.
What is the measure of ∠CBD?
1.
2.
3.
4.
50°
60°
70°
75°
28. If each interior angle of a regular polygon
measures 120°, how many sides does the polygon
have?
1.
2.
3.
4.
14
12
8
6
4
5
°
°
°
54
3
45
2
40
1
36
°
29. Which angle measure below is not a
possible measure of an exterior angle of a
regular polygon?
1. 36°
25% 25% 25% 25%
2. 40°
3. 45°
4. 54°
30. In the figure, what is the measure of ∠C?
2
3
4
5
0°
25%
11
0°
25%
10
70
1
25%
°
25%
90
70°
90°
100°
110°
°
1.
2.
3.
4.
31. TV is a diameter of circle Z.
What is the value of x?
2
3
4
5
25%
25%
10
1
25%
8
25%
6
4
6
8
10
4
1.
2.
3.
4.
32. If AP = 8 and PC = 4, what is the
measure of AB, the diameter of this circle?
4
5
25%
25%
8
3
25%
6
2
25%
4
1
2
4
6
8
2
1.
2.
3.
4.
33. TW is a diameter of circle X, and TW is parallel
to UV. If the measure of
is 25°, what is the
degree measure of
?
4
5
0°
5°
25%
21
3
25%
15
2
11
1
25%
0°
25%
13
115°
130°
155°
210°
5°
1.
2.
3.
4.
3
4
5
m
25%
5
25%
2.
2
10
1
25%
3m
25%
5
10 m
5m
3m
2.5 m
m
1.
2.
3.
4.
m
34. This is a scale drawing of a tent where 1
centimeter represents 0.5 meter. What is the
height of the tent at its highest point?
35. Which represents a two-dimensional
view from directly above the figure?
1.
25%
25%
25%
25%
2.
3.
4
5
D
3
C
2
B
1
A
4.
36. To the nearest gallon, what is the volume of a
cylindrical water heater 1.4 feet in diameter and 4
feet tall? (1 cubic foot = 7.48 gallons)
3
4
5
25%
2
ga
l
ga
l
25%
13
2
46
34
1
25%
ga
l
25%
59
34 gal
46 gal
59 gal
132 gal
ga
l
1.
2.
3.
4.
2
3
4
5
cm
3
.1
3
cm
3
42
07
cm
3
9.
14
1
7.
1.
77
cm
3
37. A spherical paintball measures 1.5
centimeters in diameter. Approximately how
much paint is in it?
1. 1.77 cm3
25% 25% 25% 25%
2. 7.07 cm3
3. 9.42 cm3
4. 14.13 cm3
38. Which proportion can be used to find the
value of PR if XMQ is similar to PRS?
1. 20/15 =
14/PR
2. 10/5 =
7/PR
3. 14/20 =
15/PR
4. 15/20 =
14/PR
3
4
5
PR
/2
/2
0
=
14
/
PR
15
/
=
=
/5
10
0
15
2
14
1
20
/1
5
=
14
/
PR
7/
PR
25% 25% 25% 25%
39. When standing upright, Gary knows his eyes are 6 feet
above ground level. To determine the depth of a well, he
stands in the position shown. Using the given measures,
how deep is the well?
2
3
4
5
ft
25%
18
ft
25%
16
12
1
25%
ft
25%
14
12 ft
14 ft
16 ft
18 ft
ft
1.
2.
3.
4.
40. The coordinates of the midpoint
of AB are -
2
3
4
5
,5
)
25%
(-2
,5
)
)
25%
(2
(5
1
25%
,3
25%
(-5
(5,3)
(-5, 3)
(2, 5)
(-2, 5)
,3
)
1.
2.
3.
4.
41. Parallelogram ABCD is placed on a coordinate
grid as shown. What is the approximate length of
diagonal AC?
3
4
5
its
0
9.
.6
4
5.
un
0
10
2
3.
un
1
25%
un
its
25% 25%
its
25%
un
3.0 units
5.4 units
9.0 units
10.6 units
its
1.
2.
3.
4.
42. Triangle A’B’C’ is A translation of
triangle ABC across
the y-axis
A 90° clockwise
rotation of triangle
ABC about the
origin
A reflection of
triangle ABC across
the y-axis
A reflection of
triangle ABC across
the x-axis
1
2
3
4
5
A
fle
c
re
re
fle
c
g.
.
tio
n
of
tr
ia
n
g.
.
of
tr
ia
n
ro
ta
t..
.
e
kw
is
lo
c
°c
90
A
A
tr
an
sl
at
io
n
of
tr
ia
n.
..
4.
A
3.
n
2.
25% 25% 25% 25%
tio
1.
43. How many different lines of
symmetry does a square have?
4
5
25%
25%
4
3
25%
3
2
25%
2
1
1
2
3
4
1
1.
2.
3.
4.
44. Which is most likely the slope
of the line graphed?
1
2
3
4
5
25%
4
/3
25%
-2
25%
/2
25%
-3
-4
-3/2
-2/3
4
-4
1.
2.
3.
4.
45. Hexagon ABCDEF is apparently
symmetric with respect to 1. Point P
only
2. Line m
only
3. Line l only
4. Both lines l
and m only
y
m
nd
ne
B
ot
h
lin
es
la
Li
ne
Li
on
lo
nl
ly
m
on
on
ly
P
in
t
Po
ly
25% 25% 25% 25%
1
2
3
4
5