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2005 Released Geometry SOL Test Study Guide



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 

The measures of some angles are given in the figure.
             mc001-1.jpg
What is the value of x?
a.
65
b.
70
c.
80
d.
85
 

 2. 

The figure shows line l intersecting lines r and s.
                      mc002-1.jpg

In the figure, Ð1 and  Ð2  are —
a.
alternate interior angles
b.
alternate exterior angles
c.
corresponding angles
d.
consecutive interior angles
 

 3. 

The Department of Transportation wants to extend the intersecting road across the highway, as indicated by the dotted line.
                             mc003-1.jpg
What should x be to ensure that the intersecting road and the new construction form a straight line?
a.
35°
b.
55°
c.
105°
d.
125°
 

 4. 

The polygon shown is convex.
mc004-1.jpg
The sum of its interior angle measures is —
a.
900°
b.
1,260°
c.
1,620°
d.
2,520°
 

 5. 

Which statement would be sufficient to prove that line l is parallel to line m?
                                mc005-1.jpg
a.
AC ^ m
b.
AB ^ l
c.
AC ^ l
d.
AB ^ AC
 

 6. 

In this diagram, line d cuts three lines to form the angles shown.
                 mc006-1.jpg
Which two lines are parallel?
a.
a and b
b.
a and c
c.
b and c
d.
No lines are parallel.
 

 7. 

Quadrilateral QRST is placed on a coordinate grid as shown.
                              mc007-1.jpg

What coordinates for S make QRST a parallelogram?
a.
(8, 6)
b.
(8, 10)
c.
(12, 6)
d.
(12, 10)
 

 8. 

Which condition will guarantee that line l is parallel to line m?
                  mc008-1.jpg
a.
Ð1  @  Ð3
b.
Ð1  @  Ð6
c.
Ð6  @  Ð5
d.
Ð3  @  Ð5
 

 9. 

The drawing shows a compass and straightedge construction of —
                            mc009-1.jpg
a.
a perpendicular to a given line from a point not on the line
b.
a perpendicular to a given line at a point on the line
c.
the bisector of a given angle
d.
an angle congruent to a given angle
 

 10. 

Which point would be on a line perpendicular to l through T?

mc010-1.jpg
a.
W
b.
X
c.
Y
d.
Z
 

 11. 

To which point should a line segment from A be drawn so that the resulting figure is a rectangle?
                   mc011-1.jpg
a.
W
b.
X
c.
Y
d.
Z
 

 12. 

DXYZ is similar to DSTR.  XY = 6 and ST = 12. If the perimeter of DSTR is 38,
then what is the perimeter of  DXYZ?
a.
19
b.
38
c.
52
d.
76
 

 13. 

Let p represent
                 mc013-1.jpg
and let q represent
                  z is a rational number.
Which is a representation of the statement below?
                       If mc013-2.jpg, then z is not a rational number.
a.
~p ® ~q
b.
p ® q
c.
p ® ~q
d.
~q ® ~p
 

 14. 

According to the Venn diagram, which statement is true?
                            mc014-1.jpg
a.
All isosceles triangles are also equilateral triangles.
b.
All equilateral triangles are also isosceles triangles.
c.
Some equilateral triangles are also isosceles triangles.
d.
No isosceles triangles are equilateral triangles
 

 15. 

Which of the following statements represents a valid argument?
a.
If a > b and a > c, then b > c.
b.
If a > b and b > c, then a > c.
c.
If a < b and a < c, then c < b.
d.
If a > b and a > c, then a > b + c.
 

 16. 

Given     mc016-1.jpg
               mc016-2.jpg
mc016-3.jpg

Which is a true proportion?
a.
mc016-4.jpg
b.
mc016-5.jpg
c.
mc016-6.jpg
d.
mc016-7.jpg
 

 17. 

Given : AD  and BC intersect at X       
            AX = XB
            CX = XD

mc017-1.jpg
Which congruency statement is true?
a.
mc017-2.jpg
b.
mc017-3.jpg
c.
mc017-4.jpg
d.
mc017-5.jpg
 

 18. 

Which list could not be the measures of lengths of the three sides of a given triangle?
a.
5 cm, 12 cm, 15 cm
b.
2 ft, 6 ft, 5 ft
c.
11 mi, 4 mi, 12 mi
d.
12 yd, 35 yd, 20 yd
 

 19. 

In the drawing of triangle XYZ, which angle has the least measure?
                     mc019-1.jpg
a.
All angles have the same measure.
b.
ÐXYZ
c.
ÐZXY
d.
ÐXZY
 

 20. 

If m ÐA = 65°, m ÐB = 15°, m ÐC = 100°, which lists the sides of the triangle in order from shortest to longest?
a.
AC, AB, BC
b.
BA, BC, AC
c.
BA, AC, BC
d.
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.
                   mc021-1.jpg

What is the distance from the boat to the dock when the rope is 25 feet?
a.
25 ft
b.
24 ft
c.
18 ft
d.
7 ft
 

 22. 

The parallelogram has the measurements shown.
                    mc022-1.jpg

Which is closest to the length of the altitude, h?
a.
19.63
b.
8.91
c.
8.67
d.
6.81
 

 23. 

For the triangle represented by the drawing below, what is the length of XZ?
                                mc023-1.jpg
a.
mc023-2.jpg
b.
mc023-3.jpg
c.
mc023-4.jpg
d.
mc023-5.jpg
 

 24. 

In rectangle ABCD, which of the following pairs of segments are not necessarily congruent?
                            mc024-1.jpg
a.
BD and AC
b.
AB and CD
c.
BC and DC
d.
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.
                      mc025-1.jpg

Which coordinates show where the fountain will be located?
a.
(2, 0.5)
b.
(0.5, 2)
c.
(3, 1.5)
d.
(1.5, 1)
 

 26. 

Quadrilateral ABCD is a parallelogram.
                  mc026-1.jpg
Which of the following must be true?
a.
AB @ AD
b.
AC @ BD
c.
Ð@  ÐD
d.
Ð@  ÐD
 

 27. 

ABCD is a rhombus.
             mc027-1.jpg

What is the measure of ÐCBD?
a.
50°
b.
60°
c.
70°
d.
75°
 

 28. 

If each interior angle of a regular polygon measures 120°, how many sides does the polygon have?
a.
14
b.
12
c.
8
d.
6
 

 29. 

Which angle measure below is not a possible measure of an exterior angle of a regular polygon?
a.
36°
b.
40°
c.
45°
d.
54°
 

 30. 

In the figure, what is the measure of ÐC?
                           mc030-1.jpg
a.
70°
b.
90°
c.
100°
d.
110°
 

 31. 

TV is a diameter of circle Z.
                mc031-1.jpg

What is the value of x?
a.
4
b.
6
c.
8
d.
10
 

 32. 

If AP = 8 and PC = 4, what is the measure of AB, the diameter of this circle?
                                mc032-1.jpg
a.
2
b.
4
c.
6
d.
8
 

 33. 

TW is a diameter of circle X, and TW is parallel to UV.
              mc033-1.jpg
If the measure of arc TU is 25, what is the degree measure of arc UV?
a.
115°
b.
130°
c.
155°
d.
210°
 

 34. 

This is a scale drawing of a tent where 1 centimeter represents 0.5 meter.
                   mc034-1.jpg
What is the height of the tent at its highest point?
a.
10 m
b.
5 m
c.
3 m
d.
2.5 m
 

 35. 

Which represents a two-dimensional view from directly above the figure?
             mc035-1.jpg
a.

mc035-2.jpg
b.

mc035-3.jpg
c.

mc035-4.jpg
d.

mc035-5.jpg
 

 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)
a.
34 gal
b.
46 gal
c.
59 gal
d.
132 gal
 

 37. 

A spherical paintball measures 1.5 centimeters in diameter. Approximately how much paint is in it?
a.
1.77 cm3
b.
7.07 cm3
c.
9.42 cm3
d.
14.13 cm3
 

 38. 

Which proportion can be used to find the value of PR if DXMQ is similar to DPRS?
                 mc038-1.jpg
a.
mc038-2.jpg
b.
mc038-3.jpg
c.
mc038-4.jpg
d.
mc038-5.jpg
 

 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.
                      mc039-1.jpg
Using the given measures, how deep is the well?
a.
12 ft.
b.
14 ft.
c.
16 ft.
d.
18 ft.
 

 40. 

The coordinates of the midpoint of AB are —
                mc040-1.jpg
a.
(5, 3)
b.
(-5, 3)
c.
(2, 5)
d.
(-2, 5)
 

 41. 

Parallelogram ABCD is placed on a coordinate grid as shown.
             mc041-1.jpg
What is the approximate length of diagonal AC?
a.
3.0 units
b.
5.4 units
c.
9.0 units
d.
10.6 units
 

 42. 

Triangle A¢B¢C¢ is —
                    mc042-1.jpg
a.
a translation of triangle ABC across the y-axis
b.
a 90° clockwise rotation of triangle ABC about the origin
c.
a reflection of triangle ABC across the y-axis
d.
a reflection of triangle ABC across the x-axis
 

 43. 

How many different lines of symmetry does a square have?
a.
1
b.
2
c.
3
d.
4
 

 44. 

Which is most likely the slope of the line graphed?
                  mc044-1.jpg
a.
mc044-2.jpg
b.
mc044-3.jpg
c.
mc044-4.jpg
d.
4
 

 45. 

Hexagon ABCDEF is apparently symmetric with respect to —
                 mc045-1.jpg
a.
point P only
b.
line m only
c.
line l only
d.
both lines l and m only
 



 
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