Regents Practice TEST 1
Interactive Version - Multiple Choice
 Geometry Level
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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.   Line k is drawn so that it is perpendicular to two distinct planes, P and R.  What must be true about planes P and R?
    [1]  Planes P and R are skew            [3]  Planes P and R are perpendicular.       
   [2]  Planes P and R are parallel.       [4]  Plane P intersects plane R but is not perpendicular to plane R.
 



2.  The vertices of  ABC are A(–1,–2), B(–1,2), and C(6,0). Which conclusion can be made about the angles of
     ABC?

[1]  m<A = m<B               [2]  m<A = m<C         [3]  m<ACB = 90      [4]  m<ABC = 60
 


3.  What is the equation of a line that passes through the point (– 3,–11) and is parallel to the line whose equation
      is 2x – y = 4?

     [1] y = 2x + 5               [2] y = 2x - 5              [3]        [4]



 
4. The diagram at the right shows the construction of the perpendicular bisector of .  Which statement is not true?
     [1]  AC = CB                [3]  AC = 2AB

     [2]             [4]  AC + CB = AB


5.  Isosceles trapezoid ABCD has diagonals and .  If AC = 5x + 13 and BD = 11x – 5, what is the value of x?

     [1]  28                                    [2]                         [3]  3                           [4]  
 


6.  The diagram below illustrates the construction of parallel to through point P. 

Which statement justifies this construction?
[1]  m<1 = m<2                     [3] 
[2]  m<1 = m<3                     [4] 

 


7.  What are the center and radius of a circle whose equation is (x – A) 2 + (y – B) 2 = C?

      [1]  center = (A,B); radius = C                             [3] center = (A,B); radius =     

      [2]  center = (– A,– B); radius = C                       [4]  center = (– A,– B); radius =



8.  A polygon is transformed according to the rule: (x, y) → ( x + 2, y).  Every point of the polygon moves two units
      in which direction?

     [1]  up                                   [2]  down                  [3]  left                        [4]  right


9.  The lines 3y + 1 = 6x + 4 and 2y + 1 = x – 9 are

     [1]  parallel         [2]  perpendicular        [3] the same line       [4] neither parallel nor perpendicular
     


10.  In which triangle do the three altitudes intersect outside the triangle?

     [1]  right triangle                  [2] acute triangle        [3] obtuse triangle         [4] equilateral triangle


11.  What is the negation of the statement “The Sun is shining”?

     [1]  It is cloudy.                            [3]  It is not raining.
     [2]  It is daytime.                          [4]  The Sun is not shining.


12.  Triangle ABC has vertices A(1,3), B(0,1), and C(4,0). Under a translation, A′, the image point of A, is
        located at (4,4). Under this same translation, point C′ is located at

     [1]   (7,1)                         [2]  (5,3)                   [3]  (3,2)                      [4]  (1,-1)


 
13. The figure in the diagram at the right is a triangular prism.
Which statement must be true?
     [1]                  [3] 

      [2]                [4]  

 

14.  Given ABC with base , median , altitude , and bisects, which conclusion is valid?

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



15.  Lines k1 and k2 intersect at point E.  Line m is perpendicular to lines k1 and k2 at point E. 
       Which statement is always true?

     [1]  Lines k1 and k2 are perpendicular.         
     [2]  Line m is parallel to the plane determined by lines
                 k1 and k2.       
     [3]  Line m is perpendicular to the plane determined by
                  lines k1 and k2.
     [4]  Line m is coplanar with lines k1 and k2.


16.  Which graph could be used to find the solution to the following system of equations?
           y = -x + 2   and    y = x2
       [1]                                                                          [3] 
                              

      [2]                                                                           [4]   
                             



17.  In the diagram at the right, circle O has a radius of 5, and CE = 2. Diameter is perpendicular to
        chord at E.  What is the length of ?
     [1]  12
     [2]  10
     [3]  8
     [4]  4


18.  Line segment has endpoints A(2,– 3) and B(– 4,6). What are the coordinates of the midpoint of ?
     [1]  (-2,3)                [2]                [3]  (-1,3)                    [4]  


19.  A rectangular prism has a volume of 3x2 + 18x + 24.  Its base has a length of x + 2 and a width of 3.
       Which expression represents the height of the prism?
     [1]   x + 4                [2]   x + 2                    [3]   3                          [4]  x2 + 6x + 8
                                 


20.  What is the slope of a line perpendicular to the line whose equation is 5x + 3y = 8?
     [1]                        [2]                            [3]                         [4] 


 
21.  In the diagram at the right, is a tangent to circle O at point S, is a secant, PS = x, PQ = 3, and PR = x + 18.  What is the length of ?
[1]  6          [2]  9          [3]  3          [4]  27
                             
 


 
22.

In the diagram below of ABC, D is a point on , AC = 7, AD = 6, and BC = 18.  The length of could be

       [1]   5                           [3]   19
       [2]   12                         [4]   25

 

 

23.  What is the measure of an interior angle of a regular octagon?
     [1]  45Ί                [2]  60Ί                  [3]  120Ί                [4]  135Ί

 


24.  The diameter of a circle has endpoints at (– 2,3) and (6,3). What is an equation of the circle?
     [1]  (x – 2) 2 + (y – 3) 2 = 16                    [3]  (x + 2) 2 + (y + 3) 2 = 16 

    [2]  (x – 2) 2 + (y – 3) 2 = 4                       [4]  (x + 2) 2 + (y + 3) 2 = 4


 
25. 

In the diagram of PRT, Q is a point on , S is a point on ,
is drawn, and .  Which reason justifies the conclusion that ? 

[1]  AA           [2]  ASA          [3]  SAS           [4]  SSS



26.  The endpoints of are A(3,2) and B(7,1). If is the result of the transformation of under
        D2  ° T– 4,3 what are the coordinates of A″ and B″ ?
     [1]  A″ (–2,10) and B″ (6,8)                  [3]  A″ (2,7) and B″ (10,5)  
     [2]  A″ (–1,5) and B″ (3,4)                    [4]  A″ (14 ,– 2) and B″ (22,– 4)


 
27. In the diagram at the right, circle A and circle B are shown.  What is the total number of lines of tangency that are common to circle A and circle B?

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


28.  Two triangles are similar, and the ratio of each pair of corresponding sides is 2 : 1. Which statement
        regarding the two triangles is not true?
     [1]  Their areas have a ratio of 4 : 1.                      [3]  Their perimeters have a ratio of 2 : 1. 
     [2]  Their altitudes have a ratio of 2 : 1.                  [4]  Their corresponding angles have a ratio of 2 : 1.
 

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