Geometry Placement Test


Please complete this online placement test accurately and honestly.  

The purpose of this assessment is to gauge your geometry skills so that we may place you in the correct course. Please do your best work, without the aid of other people or texts / alternate materials.


You have 75 minutes to complete this assessment; you will need to complete the work in one "sitting," so plan accordingly.  If you don't have 75 minutes available to you right now, close this window and come back when you are able to commit the necessary time.

You may NOT use a calculator on this assessment.

Please make every effort to complete as many questions as possible.  When you are finished, click the "Submit" button at the bottom of this page.  You will only be able to submit this form once, so be sure to review your answers before you complete the process.
 


Enter your first name and last name in the spaces provided below...

First:   Last:

Date of Birth:    Email Address:


Instructions:  Read each problem carefully and select the letter below it which corresponds to the correct answer.  You are encouraged to use a separate piece of paper on which to work while solving the problem.  There are sixty questions; you should spend no more than 75 minutes on this placement test.  Work carefully.  You may NOT use a calculator or a textbook.


1) If M is between R and T, then _________.

A)  MR +  RT = MT
B)  RM = MT
C)  RM + MT = RT
D)  MR = RT
E)  none of these


2) In a plane, two lines perpendicular to the same line are ___________ parallel.

A)  always
B)  sometimes
C)  never


3) Which of the following triangles does not exist?

I.
II.
III.
IV.

acute isosceles
right scalene
obtuse equilateral
obtuse scalene

A)  I only
B)  II only
C)  III only
D)  II and III
E)  II, III, and IV


4) Choose the statements that must be true for a rectangle.

I.
II.
III.
IV.

The diagonals are congruent.
The diagonals bisect each other.
The diagonals are perpendicular.
The diagonals bisect the angles.

A)  I and II
B)  I and III
C)  I and IV
C)  II and IV
E)  I, II, and I
V


5) If CAT  DOG, then which of the following are true?

I. A O
II. AT = DO
III. TC = GD
IV. CTA  DGO

A)  I, II, and III
B)  I, II, and IV
C)  I, III, and IV
D)  I and IV
E)  IV only


6) If two polygons are similar then which of the following must be true?

I.
II.
III.
IV.

The corresponding sides are in proportion.
The perimeters are equal.
The corresponding sides are congruent.
The corresponding angles are congruent.

A)  I and II
B)  I and IV
C)  II and III
D)  III and IV
E)  IV only


7) Which of the following methods can be used to prove a quadrilateral is a parallelogram?

I.
II.
III.
IV.

Show that both pairs of opposite angles are congruent.
Show that the diagonals are perpendicular.
Show that both pairs of opposite sides are congruent.
Show that the diagonals bisect each other.

A)  I, II, and IV
B)  I, III, and IV
C)  II, III, and IV
D)  III and IV
E)  all of these


Use the figure at the right for the next four questions (#8 - #11).

8) If r || s, then 1 is congruent to _________.

A)  9
B)  11
C)  5
D)  9 and 5


9) If 6 is congruent to 10, then _________.

A)  b || c
B)  r || s
C)  b || c and r || s
D)  none of these


10) If  3 is congruent to 12, then _________.

A)  b || c
B)  r || s
C)  b || c and r || s
D)  none of these

 

11) If b || c, then 6 must be _________ to 3.

A)  congruent
B)  supplementary
C)  congruent and supplementary
D)  adjacent
E)  congruent and adjacent

 


12) If two angles of a triangle measure 47 and 93, then the measure of the third angle is _______.

A)  46
B)  30
C)  50
D)  60
E)  none of thes
e


13) The sum of the measures of the exterior angles, one at each vertex, of a convex octagon is _______.

A)  135
B)  1080
C)  45
D)  360
E)  none of thes
e


14) Find the measure of each interior angle of a regular polygon with 10 sides.

A)  144
B)  180
C)  36
D)  135
E)  none of these


15) In parallelogram ABCD, BCD is congruent to _______.

A)  BAD
B)  DBA
C)  DAB
D)  ADB


16) The diagonals of a trapezoid ________ bisect each other.

A)  always
B)  sometimes
C)  never


17) If the corresponding angles of two polygons are congruent, then the polygons are ________ similar.

A)  always
B)  sometimes
C)  never


18) If the lengths of the bases of a trapezoid are 19 and 33, then the length of the median is ________?

A)  52
B)  14
C)  26
D)  21
E)  none of these


19) If the lengths of two sides of a triangle are 7 and 13, then the length of the third side must be between ______.

A)  8 and 12
B)  7 and 19
C)  7 and 20
D)  6 and 20
E)  none of these


20) In ABC, mA = 4x + 5, mB = 2x + 20, and mC = 5x - 10.  The congruent sides of the triangle are _______.

A)  and 
B)  and 
C)  and 
D)  , , and 
E)  none of these


21) If ABCD is a parallelogram, then which of the following must be true?

A)  D
B)   
C)   
D)  mB + mC = 180


22) In QRS, QR = 6, RS = 7, and QS = 8.  The largest angle of the triangle is _______.

A)  Q
B)  R
C)  S
D)  the answer cannot be determined


23) The ratio of the measures of two complementary angles is 4 : 11.  The measure of the larger angle is _______.

A)  48
B)  66
C)  24
D)  132
E)  none of these


24) If r : s = 3 : 7, then r : 3 = _______.

A)  s : 7
B)  7 : s
C)  r : 7
D)  s : 3
E)  7 : 3


Use the figure at the right for the next two questions (#25 - #26).

25) If CE = 12, then BD = _______.

A)  4
B)  6
C)  8
D)  9



26) If BD = 8, then DE = _______.

A)  12
B)  14
C)  16
D)  18


27) In DEF, if  , bisects EDF, and X lies on , then mDXE = _______.

A)  120
B)  70
C)  80
D)  90
E)  the answer cannot be determined


28) In RSQ, if bisects QSR, then RT = _______.

A   6
B   9
C   12
D   15



29) In the given figure, the shortest segment is _______.

A   AB
 BC
C   BD
 CD
 AD >


30) If QRS ~ XYZ, QR = 9, RS = 12, QS = 14, and YZ = 18, then the scale factor of QRS to XYZ is _______.

A)  1 : 2
B)  2 : 3
C)  7 : 9
D)  3 : 4
E)  none of these


Use the figure at the right for the next FIVE questions (#31 - #35).

31) If AB = 6 and BC = 8, then AC = _______.

A)  9
B) 
C)  10
D) 


32) If mA = 60 and AB = 5, then BC = _______.

A) 
B)  10
C) 
D)  5


33) If mDBC = 45 and BC = 7, then BD = _______.

A)

B)
C)
D) 7
E)

34) In ABC, tan A = _______.

A) 
B)
C) 
D) 


35) In ABC, which proportions are true?

I.
II.
III.

A)  I only
B)  II only
C)  III only
D)  II and III
E)  none of these


36) A triangle with sides of lengths 8, 9, and 12 is a(n) ________ triangle.

A)  acute
B)  right
C)  obtuse
D)  equiangular
E)  The answer cannot be determined.


37) Using only the angle of elevations of the sun and the length of the shadow of a tree, which trigonometric function could be used to find the height of a tree?

A)  sine
B)  cosine
C)  tangent


38) In a circle with radius 12 and m = 120, the length of = _______.

A)  48π
B)  12π
C)  16π
D)  8π
E)  none of these


39) The area of a regular polygon with perimeter 48 and apothem is _______.

A) 
B) 
C) 
D) 
E)  none of these


40) If the ratio of the lengths of the corresponding sides of two similar polygons is 2 : 3, then the ratio of their areas is _______.

A)  8 : 12
B)  4 : 6
C)  2 : 3
D)  4 : 9
E)  none of these


41) The area of a 45 - 45 - 90 triangle with one leg of length 8 is _______.

A)  16
B)  32
C) 
D)  64
E)  none of these


42) A segment whose endpoints are points of a circle must be a _______ and can be a _______.

A)  chord, secant
B)  diameter, radius
C)  secant, chord
D)  chord, diameter


Use the figure at the right for the next TWO questions (#43 - #44).

43) In circle P, if mE = 65, then mC = _______,

A)  65
B)  115
C)  135
D)  130
E)  none of these


44) In circle P, which of the following segments must be congruent?

I.
II.
III.
IV.

A)  II and IV
B)  III and IV
C)  I, II, and III
D)  II, III, and IV
E)  all of these


Use the figure at the right for the next THREE questions (#45 - #47).
  • O is the center of the circle
  • the measure of arc AE = 100
  • the measure or arc AB = 30
  • the measure of arch BC = 80

45) m3 = ______.

A)  60
B)  65
C)  70
D)  90
E)  none of these


46) If AF = 10, AD = 13, and CF = 5, then EF = _______.

A)  26
B)  11
C)  15
D)  6
E)  none of these


47) If GC = 12, GB = 4, and GA = 3, then GD = _______.

A)  11
B)  14
C)  16
D)  9
E)  none of these


48) In circle P at the right, if QS = 20, and US = 4, then TR = _______.

A)  12
B)  8
C)  16
D)  The answer cannot be determined.


49) π is the ratio of the _______ of a circle to its _______.

A)  area, circumference
B)  diameter, circumference
C)  circumference, diameter
D)  circumference, radius


50) The area of a trapezoid with height 10 and bases 9 and 13 is _______,

A)  55
B)  220
C)  110
D)  27
E)  none of these


51) A square is inscribed in a circle of radius 10.  What is the area of the square?

A)  100
B)  200
C)  400
D)
E)  none of these


52) One side of a rectangle has length 12, and the rectangle has area 60.  What is its perimeter?

A)  17
B)  30
C)  34
D)  36
E)  none of these


53) The lateral area of a regular hexagonal prism with base edge 5 and height 10 is _______,

A)  250
B)  300
C)  400
D)  500
E)  none of these


Use the figure at the right for the next TWO questions (#54 - #55).

54) The regular square pyramid shown has a slant height of _______.

A) 
B) 
C) 
D)  13


55) The regular square pyramid shown has a volume of _______.

A)  200
B)  400
C)  600
D)  800


56) Two similar pyramids have heights of 4 and 10.  The ratio of their volumes is _______.

A)  2 : 5
B)  6 : 15
C)  4 : 25
D)  8 : 125
E)  none of these


For the next FOUR questions (#60 - #63), use the coordinates shown:

57) AD = _______.

A)  11
B)
C)
D)  10

  • A (0, 3)

  • B (4, 1)

  • C (-2, -1)

  • D (7, 7)

  • E (1, -1)


58) Which pair of lines are perpendicular?

A) 
B) 
C) 
D) 
E)  none of these

59) An equation of in slope-intercept form is _______.

A)   y = 2x - 3
B)   y = 2x + 3
C)   y = x + 3
D)   y = -x + 3
E)   none of these


60) The midpoint of has coordinates _______,

A)  (3, 4)
B)  (4, 3)
C)  (3, 3)
D)  (4, 4)
E)  none of these


   
How many minutes has it taken you to complete your work to this point?   
   

I have completed this work on my own, without assistance, and within the time allowed (seventy-five minutes) and without the use of textbooks or calculators.

The statement above is true.

Signed:

 

                                        (type your full name here)


Asheville School Technology.
Last revised: May 14, 2009