Name: 
 

2014 Geometry SOL Practice Worksheet b


 1. 
Let p represent:
         Two angles are vertical angles.
Let q represent:
         The angles are congruent.

What is the symbolic representation of the following statement?
     If two angles are congruent, then the angles are vertical angles.
a.
mc001-1.jpg
b.
mc001-2.jpg
c.
mc001-3.jpg
d.
mc001-4.jpg
 

 2. 
Richie is drawing the
perpendicular bisector of mc002-1.jpg.
          

Which point is on the perpendicular bisector of mc002-2.jpg?		mc002-3.jpg
a.
H
b.
S
c.
D
d.
X
 

 3. 
In this figure, parallel lines h and d
are intersected by line z.
                    
Which pair of angles is NOT supplementary?		mc003-1.jpg
a.
mc003-2.jpg and mc003-3.jpg
b.
mc003-4.jpg and mc003-5.jpg
c.
mc003-6.jpg and mc003-7.jpg
d.
mc003-8.jpg and mc003-9.jpg
 

 4. 
What type of construction
is illustrated in the figure?mc004-1.jpg
             
a.
The bisection of mc004-3.jpg
c.
An angle congruent to mc004-5.jpg
b.
The bisection of mc004-4.jpg
d.
A line segment congruent to mc004-6.jpg
 

 5. 
The Venn diagram represents students
who play instruments in the orchestra.
                          
Identify each region of the Venn diagram that represents students who play only the clarinet and the flute.		mc005-1.jpg
a.
none
b.
6
c.
8
d.
6, 7, 8, 10
 

 6. 
An angle congruent to 
angle M is being constructed.
       
    
Which ray could be drawn to construct an angle congruent to mc006-1.jpg ?		mc006-2.jpg
a.
mc006-3.jpg
b.
mc006-4.jpg
c.
mc006-5.jpg
d.
mc006-6.jpg
 

 7. 
Which diagram shows a pair of angle measures that prove lines d and s are parallel?
a.
mc007-1.jpg
c.
mc007-3.jpg
b.
mc007-2.jpg
d.
mc007-4.jpg
 

 8. 
Which is a valid conclusion that can be drawn from these statements?

If a quadrilateral is a rectangle, then it is a parallelogram.
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
a.
Every quadrilateral is a rectangle.
b.
Every parallelogram is a rectangle.
c.
Opposite angles of a rectangle are congruent.
d.
Opposite angles of a quadrilateral are congruent.
 

 9. 
This figure show parallel
stair railings through points N, B, X, and U.
                         
What is the value of x ?		mc009-1.jpg
a.
25
b.
45
c.
65
d.
115
 

 10. 
Given D (–1, 8) and R (7, –6)

        
What is the length of mc010-1.jpg ?		mc010-2.jpg
a.
mc010-4.jpg
b.
mc010-5.jpg
c.
mc010-6.jpg
d.
mc010-7.jpg
 

 11. 
Line c contains the points
(–8, 6) and (6, –1). 



Plot a point other than point F with integral coordinates that is on a line parallel to c and passes through point F.		mc011-1.jpg
                    
a.
(–8, –1)
b.
(–7, –1)
c.
(–8, –2)
d.
(–9, –1)
 

 12. 
Which best describes
the construction in the diagram shown?mc012-1.jpg
               
a.
The bisector of a line segment
b.
A line segment congruent to a given line segment
c.
A perpendicular to a given line at a point on the line
d.
A perpendicular to a given line from a point not on the line
 

 13. 
What is the inverse of the following statement?

If the measure of an angle is 90º, then it is a right angle.
a.
If the measure of an angle is not 90º, then it is not a right angle.
b.
If it is not a right angle, then the measure of an angle is not 90º.
c.
If it is a right angle, then the measure of an angle is 90º.
d.
If the measure of an angle is not 90º, then it is a right angle.
 

 14. 
Quadrilateral CTXF is shown.

   
If CTXF is reflected across the line mc014-1.jpg, what are the coordinates of X’ ?		mc014-2.jpg
a.
mc014-6.jpg
b.
mc014-7.jpg
c.
mc014-8.jpg
d.
mc014-9.jpg
 

 15. 
Line k and g are cut by a transversal

   
What value of x proves that k // g ?


mc015-1.jpg
mc015-2.jpg
a.
35
b.
36
c.
46
d.
45
 

 16. 
Given :  D(–5, 5) and Z(2, 8)                      What is the slope of mc016-1.jpg?
a.
mc016-4.jpg
b.
mc016-5.jpg
c.
mc016-6.jpg
d.
mc016-7.jpg
 

 17. 
For which polygon are both mc017-1.jpg and mc017-2.jpg lines of symmetry?
a.
mc017-3.jpg
c.
mc017-5.jpg
b.
mc017-4.jpg
d.
mc017-6.jpg
 

 18. 
The figure represents a ramp
with handrails. 
Segments FG and JK are parallel to MN. 
Segments GH and KL are parallel to NP. 
Segments FM and GN are parallel to HP.

                     
If mc018-1.jpg, what is mc018-2.jpg ?		mc018-3.jpg
a.
69º
b.
90º
c.
111º
d.
159º
 

 19. 
Laura attached a wire
between two poles on a hill as shown.
           
Which is closest to x, the distance between the two poles?		mc019-1.jpg
a.
22 ft
b.
23 ft
c.
64 ft
d.
77 ft
 

 20. 
Triangles FMC, FDC, and WMC
are show on the coordinate grid, and all the vertices have coordinates that are integers.
            
Which statement is true?		mc020-1.jpg
a.
No two triangles are congruent.
b.
Only mc020-2.jpg and mc020-3.jpg are congruent.
c.
Only mc020-4.jpg and mc020-5.jpg are congruent.
d.
Triangle FMC, mc020-6.jpg, and mc020-7.jpg are all congruent
 

 21. 
The lengths of two sides of a triangle are 23 inches and 43 inches.  What is the range of possible lengths, in inches, for the third side, x, of this triangle?
                                                 mr021-1.jpg
 a.
10
 c.
58
 e.
50
 g.
66
 b.
20
 d.
35
 f.
76
 h.
89
 

 22. 
Which of the following sets of lengths can represent the measures of the sides of a right triangle?
a.
4, 5, 7
b.
5, 10, 13
c.
8, 13, 17
d.
21, 28, 35
 

 23. 
Given the measures shown in the diagram, which two triangles are congruent?
mc023-1.jpg         mc023-2.jpg
a.
F and R
b.
A and V
c.
A and R
d.
F and V
 

 24. 
Part of a marching band formed by a triangle made with trombone players on one side, tuba players on one side, and oboe players on the third side.
     •  The angle formed by the trombone and oboe players measured 41º
     •  The angle formed by the oboe and tuba players measured 72º
Which orders the sides of this triangle from least to greatest using the instrument names?
a.
tuba, trombone, oboe
c.
trombone, oboe, tuba
b.
tuba, oboe, trombone
d.
oboe, trombone, tuba
 

 25. 
An equilateral triangle is folded in half.


What is x, the height of the equilateral triangle?		mc025-1.jpg
a.
mc025-5.jpg m
b.
22 m
c.
mc025-6.jpg m
d.
11 m
 

 26. 
Look at this triangle.

Which triangle is similar to the given triangle?		mc026-1.jpg
a.
mc026-2.jpg
c.
mc026-4.jpg
b.
mc026-3.jpg
d.
mc026-5.jpg
 

 27. 
Click and drag each selected reason to the correct box
Given:  Figure EXWR with diagonal mc027-1.jpg
           mc027-2.jpg; mc027-3.jpg

Complete the proof of mc027-4.jpg by selecting the reasons for the last two statements.		mc027-5.jpg

Statements
Reasons
 
mc027-6.jpg

mc027-7.jpg


Given
 


mc027-8.jpg
  


mc027-9.jpg
  
a.
Given and SSS
e.
Reflexive and SAS
b.
Dfn of congruent triangles and HL
f.
Given and Dfn of congruent triangles
c.
Reflexive and SSS
g.
Reflexive and HL
d.
Given and SAS
h.
Dfn of congruent triangles and SSS
 

 28. 
A spectator is viewing the six cars
of a roller coaster as it travels down a hill at an amusement park.
                      
Which is the closest to the total length of the six cars?		mc028-1.jpg
a.
15.3 ft
b.
16.2 ft
c.
24.7 ft
d.
44.2 ft
 

 29. 
Three triangles that do not overlap
are shown on the coordinate grid.  The coordinates of all vertices are integers.


                 
Which statement is true?		mc029-1.jpg
a.
mc029-2.jpg
b.
mc029-3.jpg
c.
mc029-4.jpg
d.
mc029-5.jpg
 

 30. 
Using the information given,
which congruence postulate or theorem can be used to prove that mc030-1.jpg ?mc030-2.jpg
a.
Hypotenuse-Leg Theorem
c.
Side-Angle-Side Postulate
b.
Side-Side-Side Postulate
d.
Angle-Angle-Side Theorem
 

 31. 
Which could be the lengths of three sides of a triangle?
a.
9 ft, 3 ft, 6 ft
c.
8 ft, 20 ft, 15 ft
b.
22 ft, 11 ft, 8 ft
d.
21 ft, 12 ft, 8 ft
 

 32. 
Given:  T lies on mc032-1.jpg and C lies on mc032-2.jpg

     
Which condition proves mc032-3.jpg ?		mc032-4.jpg
a.
mc032-5.jpg
c.
mc032-7.jpg
b.
mc032-6.jpg
d.
mc032-8.jpg
 

 33. 
Given:  Parallelogram YZRU where
mc033-1.jpg and mc033-2.jpg.
                            
What value of x proves this parallelogram is a rhombus?		mc033-3.jpg

mc033-4.jpg
a.
30
b.
5
c.
4
d.
–4
 

 34. 
The floor plan for a modern home
is modeled by the composite of the regular octogon and triangle shown.

What is closest to the measure of mc034-1.jpg ?		mc034-2.jpg
a.
155º
b.
165º
c.
160º
d.
175º
 

 35. 
Given:  Circle J with center at (–3, –1)
What equation could represent circle J?
a.
mc035-4.jpg
c.
mc035-6.jpg
b.
mc035-5.jpg
d.
mc035-7.jpg
 

 36. 
This container is composed
of a right circular cylinder and a right circular cone.
                            
Which is closest to the surface area of the contianer?		mc036-1.jpg
a.
1071 in²
b.
1832 in²
c.
2212 in²
d.
1451 in²
 

 37. 
Given:  Circle P


What is the value of y?		mc037-1.jpg
a.
33
b.
52
c.
85
d.
95
 

 38. 
A tablet computer box in the shape of a rectangular
prism is shown. The height of the box is 2 cm.

The height of the original box will be increased by 1.5 centimeters so a new instruction manual and an extra battery can be included.  Which is closest to the total surface area of the new box?		mc038-1.jpg
a.
561 cm²
b.
592 cm²
c.
468 cm²
d.
685 cm²
 

 39. 
Parallelogram NBVY is a
rhombus with mc039-1.jpg

What is the mc039-2.jpg ?		mc039-3.jpg
a.
36°
b.
54°
c.
108°
d.
144°
 

 40. 
Circle C has a center at (3, –5) and a diameter of 10 units.  Which point lies on circle C?
a.
(6, –1)
b.
(3, –5)
c.
(11, 1)
d.
(13, 5)
 

 41. 
An architect used this diagram to
design a curved balcony.  She drew a circle with a radius of 44 feet and a central angle of 60° to determine the length of railing needed for the balcony.

Which is the closest to the length of railing needed for the curved section of the balcony?		mc041-1.jpg

a.
23 ft
b.
47 ft
c.
276 ft
d.
1014 ft
 

 42. 
A polygon is shown:


What is the measure of mc042-1.jpg ?		mc042-2.jpg
a.
66°
b.
90°
c.
114°
d.
228°
 

 43. 
The volume of a cube is 125 cubic centimeters.  What is the surface area of the cube?
a.
25 cm²
b.
150 cm²
c.
625 cm²
d.
750 cm²
 

 44. 
The diagonals of rectangle GXJK intersect
at the point (1, 3).  One of the vertices of the rectangle GXJK is located at (–3, 5).
            
Which of the following could be the location of another vertex of this rectangle?		mc044-1.jpg
a.
(5, 1)
b.
(–1, 4)
c.
(1, 5)
d.
(1, 1)
 

 45. 
Given: Circle X

             
Which is the closest to the area of the shaded sector of circle X ?		mc045-1.jpg
a.
28 cm²
b.
168 cm²
c.
284 cm²
d.
452 cm²
 

 46. 
The ratio of the lengths of the radii of two sphere is 3:8.  What is the ratio of the volumes of these two spheres?
                        mr046-1.jpg
 a.
1
 c.
8
 e.
24
 g.
27
 b.
3
 d.
9
 f.
64
 h.
512
 

 47. 
This figure is composed of
an isosceles trapezoid and a regular octagon.
        
What is the value of x ?		mc047-1.jpg
a.
98
b.
119
c.
106
d.
172
 

 48. 
Click on the grid to plot the point you want to select.

Plot the center of the circle defined by the equation:          mc048-1.jpg		mc048-2.jpg
a.
(–5, 8)
b.
(5, –8)
c.
(5, 8)
d.
(–5, –8)
 

 49. 
A rectangular pyramid is shown.

      
What is the volume of the pyramid?		mc049-1.jpg
a.
1920 ft³
b.
960 ft³
c.
640 ft³
d.
240 ft³
 

 50. 
A company is creating a new cylinderical container to replace its original cylindrical container.
     •  The new container will have 16 times the volume of the original container.
     •  The height of the new container will remain the same as the height of the original container.
The length of the radius of the new container will be --
a.
4 times the length of the radius of the original container
b.
16 times the length of the radius of the original container
c.
64 times the length of the radius of the original container
d.
256 times the length of the radius of the original container
 



 
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