Multiple Choice Practice
 Parallels and Quadrilaterals
Geometry Level
 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 parallelogram CARS,  m<C = 5x - 20  and  m<A = 3x + 40.  Find the value of x.
       [1]  15                [2]  20                 [3]  30                [4]  130

 

 

 2.   In the accompanying diagram,
What is the value of x.
     [1]  10                [2]  17.5
     [3]  40                [4]  50

 


3.  If two consecutive sides of a rhombus are represented by  3x - 6  and  x + 14,  then the perimeter of the rhombus is

     [1]  10           [2]  24                  [3]  70               [4]  96




 

4.  Points A, B, C, and D are midpoints of the sides of square JETS.  If the area of JETS is 36, the area of ABCD is    
     [1] 
      [2] 
     [3]  9
     [4]  18

 

 

5.  In the diagram at the right, parallel lines a and m are cut by transversal t, m<1 = 4x + 16 and m<2 = 2x - 22.  Find m<1.
     [1]  31°
     [2]  40°
     [3]  140°
     [4]  148°

 

 

6.  A quadrilateral must be a parallelogram if one pair of opposite sides is
     [1]  congruent, only.
     [2]  parallel, only.
     [3]  congruent and parallel.
     [4]  parallel and the other pair of opposite sides is congruent.


 

7.  The perimeter of a rhombus is 60.  If the length of its longer diagonal measures 24, the length of the shorter diagonal is

    [1]  20                [2]  18               [3]  15                [4]  9




 

8.  In the diagram at the right, lines a and m are parallel with transversal t.  Find the number of degrees in the angle labeled x. 
      [1]  80°
     [2]  100°
      [3]  120°  
     [4]  140°



 

9.  In the accompanying diagram of rectangle ABCD, m<ABE = 30 and m<CFE = 144. Find m<BEF.
     [1]  36°                 [2]  60°                    
     [3]  84°                 [4]  90°


 

10. Find the perimeter of a rhombus whose diagonals measure 12 and 16.

     [1]  10                  [2]  20                   [3]  40                   [4]  80
 


 

11.  In the diagram at the right, lines a and m are parallel and are cut by transversal t.  Which two angles are not always congruent?
      [1]  <4 and <6
     [2]  <1 and <8  
     [3]  <4 and <5
     [4]  <2 and <3


 

 

12.  In the diagram at the right, line a is parallel to line b, and line t is a transversal.  If m<1 = 97 and m<2 = 44, find m<3.
      [1]  44 
      [2]  53   
      [3]  83   
      [4]  97

 

 

13.  In the diagram at the right, lines f and g are parallel, and lines a and b are parallel.  The
m<x = 75.  What is the value of  m<y + m<z ?
      [1]  75
      [2]  105
     [3]  150
     [4]  180 


 

14.  Which statement is true about all parallelograms? 
      [1]  The diagonals are congruent.  
      [2]  The area is the product of two adjacent sides.
      [3]  The opposite angles are congruent.
      [4]  The diagonals are perpendicular to each other.

 

 

15.  Which property is true for all trapezoids?
     [1]  Only two opposite sides are parallel.
     [2]  Consecutive angles are supplementary.
     [3]  The base angles are congruent.
     [4]  All angles are equal.

 

 
16.  In the diagram at the right, ABCD is a square,
 
What is m<DAE ? 
     [1] 22.5
     [2] 45.0
     [3] 112.5
     [4] 135.0


17.  Side of parallelogram ABCD is represented by the equation
Which equation could represent side ?

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

 

18.  In rectangle DATE, diagonals and intersect at S.  If AE = 40 and ST = x + 5, find the value of x.
      [1]  10               [2]  15              [3]  18               [4]  20   

 

 
19.  A parallelogram must be a rectangle if its diagonals 
    [1]  bisect each other.   
    [2]  bisect the angles to which they are drawn.
    [3]  are perpendicular to each other. 
    [4]  are congruent.

 

 
20.  In the accompanying diagram of rhombus ABCD,  m<CAB = 35.   Find m<CDA.
      [1] 35
      [2] 70  
      [3] 110
     [4] 140  

 

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