Regents Practice TEST 3
Interactive Version - Multiple Choice
 Geometry Level
 Return to Test List | Geometry Index | Regents Exam Prep Center
 

Directions:  Choose the best answer.  Answer ALL questions (or only a few at a time), then use the BUTTON at the BOTTOM of the page to check your answers.  If you are told that an answer is incorrect, go back and redo that question and CHECK ANSWERS again.   You may CHECK ANSWERS at any time.
You may use your graphing calculator when working on these problems.
1.   In two similar triangles, the ratio of the lengths of a pair of corresponding sides is 7:8. If the perimeter of the larger
      triangle is 32, find the perimeter of the smaller triangle.  
    [1]  8                           [2]  16                      [3]  21                   [4]  28
 



2.  Which of the following statements is NOT true about the centroid of a triangle?

    [1]  The centroid of a triangle is point where the medians of the triangle are concurrent.
    [2]  The centroid of a triangle may be located inside the triangle, on a side of the triangle, or outside of the triangle.
    [3]  The centroid of a triangle divides the medians of the triangle into a ratio of 2:1.
    [4]  The centroid of a triangle is the center of gravity of a triangular shape of uniform thickness and density.
 


3.  Point C (3,4) is the midpoint of .  If the coordinates of A are (7,6), the coordinates of B are:   

     [1]  (-1,2)                     [2]  (2,1)                      [3]  (5,5)                  [4]  (11,8)



 
4.

In , is extended to E, and D is a point on .

[1]  m<ADE > m<ABC     [3]  m<ACB = m<ABC
[2]  m<ADE = m<ABC    [4]  m<ABC > m<ADE


5.  If the lengths of two sides of a triangle measure 7 and 15, then the length of the third side could measure:

     [1]  7                                  [2]  8                       [3]  11                           [4]   24
 


6.  In the accompanying diagram of right triangle ABC, altitude divides hypotenuse into segments with lengths
      of 4 and 5.  Find the length of leg .
[1]  4.5     [2]          [3]  6       [4]  7.5

 


 
7.  In the accompanying diagram, 
        
    
       [1]  95º                         [2]  100º                     [3] 120º                   [4]  140º



8.  If the measures of three angles of a triangle are represented by (y + 30)°, (4y + 30)°, and (10y – 30)°, then the
      triangle must be:

     [1]  obtuse                      [2]  isosceles               [3]  scalene              [4]  right


9.  The number of points equidistant from two parallel lines and also equidistant from two points on one of the given lines
      is exactly:

     [1]  1                              [2]  2                            [3]  3                      [4]  4
     


10.  The lengths of the bases of an isosceles trapezoid are 6 centimeters and 12 centimeters. If the length of each leg is
        5 centimeters, what is the area of the trapezoid?

     [1]  18 cm2                  [2]  36 cm2                    [3]  45 cm2              [4]  90 cm2


 

11.  In the accompanying diagram, and are tangents drawn
        to circle O, and chord  is drawn.  If m<P = 40, what is
        m<PQS?

 
      [1]  140º                  [2]  80º                       [3]  70º                        [4]   60º                      



12.  Which statement is logically equivalent to “If Andrea gets a job, she buys a new car”?

       [1]   Andrea gets a job and she buys a new car.
       [2]   If Andrea does not buy a new car, she does not get a job.
       [3]   If Andrea does not get a job, she does not buy a new car.
       [4]   If Andrea buys a new car, she gets a job.


 
13.

In the accompanying diagram, and intersect at E,
E is the midpoint of  , and .  Which statement can be
used to prove that ?

[1]  ASA (Angle-Side-Angle)       [3]  SSS (Side-Side-Side) 
 [2]  HL (Hypotenuse-Leg)           [4]  SAS (Side-Angle-Side)
     

 

 

 

14.  For this rectangular solid, which plane(s) contain D and are parallel to plane FEH?
 [1]  planes DAB and HAD 
[2]  planes DCB and FCB 
 [3]  only plane DAB
 [4]  only plane HAD

             



 

15.  In the accompanying diagram of circle O, chords and intersect at E and .  What is the m<DEB?
      [1]  36º        [2]  90º       [3]  100º         [4]  126º

     
 


16.  The sum of the measures of the interior angles of a regular pentagon is:
       [1]  180º                  [2]  360º                   [3]  540º                    [4]  720º 
                             


 
17.  Which statement is false about the line whose equation is y = -2x - 5 ?

        [1]  Its slope is -2.
        [2]  It is parallel to the line whose equation is  y = 2x + 5.
        [3]  Its y-intercept is -5.
        [4]  It is perpendicular to the line whose equation is  . 



 
18.  In the accompanying diagram, ABC is an equilateral triangle with a perimeter
        of 30.   What is the length of altitude h of this triangle?
      [1]          [2]       [3]          [4] 


19.  Which of the following points is a solution to the system   y = 4 - x   and   y = -x2 + 2x + 4 ?
     [1]   (1,3)                  [2]   (4,0)                        [3]  (-1,-3)                      [4]  (3,1) 
                                 


20.  Which equation represents a circle with center (1,–3) and radius 4?
        [1]  (x - 1)2 + (y + 3)2 = 16                    [3]  (x + 1)2 + (y - 3)2 = 16     

        [2]  (x - 1)2 + (y + 3)2 = 4                       [4]  (x + 1)2 + (y - 3)2 = 4 



 
21.  The diagram at the right shows the construction of a perpendicular,
, to a line l from point P.  The arc drawn from point P intersects line l at A and B, and the arcs drawn from points A and B intersect  at C.  Which of the statements is not always true about this construction?
[1]  PA = PB
 [2]  AX = BX
 [3]  PX = CX
[4]  AC = BC                            



 
22.

The distance between points (4a,3b) and (3a,2b) is
  [1]             [2]           [3]  a + b            [4]  
  

 

23.  A translation maps (x, y) to (x – 5, y + 3). In which quadrant does the point (–3,–2) lie under the same translation?
       [1]  I                       [2]  II                       [3]  III                   [4]  IV

 


24.  What is the equation of a line that passes through the point (-3,2) and is parallel to the line 2x - 3y = 12?
     [1]  y = 2x - 4            [2]              [3]              [4]    


 
25. 

The sentence "If __________, then 6 + 3 = 9." is TRUE.  Which of the following statements could be used to fill the blank and maintain the truth value of the sentence?
 [1]  10/5 = 2
[2]  12/3 = 6
[3]  both choice [1] and choice [2] could be used
[4]  neither choice [1] nor choice [2] could be used  



26.  A triangle has vertices A(3,2), B(4,1) and C(4,3).  What are the coordinates of point B under the glide reflection
       

       [1]  (2,-4)              [2]  (4,0)                         [3]  (4,2)                  [4]  (-4,2)


 
27. The sphere appears in nature whenever a surface wants to be as small as possible.  For this problem, assume that a bubble is a sphere.  If the diameter of the bubble is known to be 2 mm, what is the surface area of the bubble to the nearest square mm ?

[1]   13                 [2]  25                          [3]  28                       [ 4]  52

 


28.  Under a dilation of scale factor 3 with the center at the origin, what will be the coordinates of the image of point
        B(2,3)?
     [1]  (6,3)                  [2]  (2,9)                        [3]  (5,6)                    [4]  (6,9)
 

Return to Test List | Geometry Index | Regents Exam Prep Center