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					Plane Geometry                                                      PRACTICE Chapter 6 Test
1. You will match the following vocabulary terms with their definitions (there are 12 terms and
   10 definitions, so 2 terms will not be used):

        i. concave                               v. vertex of a polygon    ix. rectangle
        ii. convex                               vi. quadrilateral         x. rhombus
        iii. regular polygon                     vii. kite                 xi. parallelogram
        iv. diagonal                             viii. trapezoid           xii. square

MULTIPLE CHOICE – circle the letter of the correct answer.
              2. Which of the following terms does NOT describe the figure?

                           a. concave                         b. hexagon
                           c. polygon                         d. regular



3. Which of the following is the sum of the measures of the interior angles of a 5-sided convex
   polygon?

   a. 72°                              b. 360°                  c. 540°           d. 900°

4. Which of the following is the value of “a”?

   a. 78                    b. 109               c. 60          d. 53


5. The diagonals of the parallelogram ABCD intersect at point X. Which of the following is NOT
   true? [hint – try drawing a picture to be sure!]

   a. DAB  BCD                                b. mDAB  mCBA  180

   c. BC  AD                                    d. AX  XB

Use the figure below for problems 6 and 7.




6. WXYZ is a parallelogram. Which of the following is the measure of W?

   a. 68°                              b. 112°                  c. 61°            d. 7°

7. WXYZ is a parallelogram. Which of the following is the value of x?

   a. 68                               b. 10                    c. 8.5            d. 7
8. Which of the figures must be a parallelogram (according to the
   given markings)?

   a. Figure 1 only                  b. Figure 2 only
   c. Both Figure 1 and Figure 2     c. Neither Figure 1 nor Figure 2


                      9. If you know that EF GH , which of the following pieces of
                          information would allow you to conclude that EFGH is a
                          parallelogram?

                      a. EF  GH                        b. FG  EH

10. Which of the following is NOT always true?

   a. A square is a rhombus                    b. A rectangle is a parallelogram
   c. A rhombus is a rectangle                 d. A square is a rectangle

11. PQRS is a rectangle and PR  26 . Which of the following is
   the value of x?

   a. 6.5             b. 13          c. 26              d. 52


                      12. JKLM is a rhombus. If mJML  70 , which of the following is the
                         value of mJKM ?

                      a. 35°                   b. 55°                c. 70°             d. 110°


13. If you’re given that ABCD is a parallelogram, AC  BD , and AB  CD ,
   which of the following best describes the figure?

   a. kite                           b. rhombus
   c. square                         d. rectangle


                          14. Which of the following best describes the figure?

                          a. kite                           b. parallelogram
                          c. quadrilateral                         d. trapezoid

15. Which of the following is the measure of F in the isosceles
   trapezoid?

   a. 79°             b. 101°        c. 180°            d. 360°
16. In trapezoid PQRS, which of the following is the length of midsegment
    XY ?

    a. 48 cm            b. 51 cm                d. 17 cm                  d. 31 cm


FREE RESPONSE/SHORT ANSWER – follow all directions
                   17. Use the polygon at the left to answer the following:
                                a. Name the polygon by the number of sides.


                                        ___________________
                                b. Is the polygon concave or convex?


         ___________________
    c. Is the polygon regular or irregular?

                                                                          ___________________

18. Find the measure of each interior angle of a regular hexagon.


                                                                                       ___________

19. Find the value of “n” in the figure at the right.


                                                        ____________

20. Write a biconditional statement to define the term “rectangle”.

    ______________________________________________________________________

    ______________________________________________________________________

21. ABCD is a parallelogram. Use it to do the following:
    a. What’s the justification for the equation “ 15x  5  16x  2 ”?

                                    _______________________
    b. Find mD .
                                                        mD  _____
    c. What’s the justification for the equation “ 16x  2  12y  10  180 ”?
                                                                ______________________
    d. Find the value of y.
                                                                               y  _____

                                    22. PQRS is a parallelogram. Use it to do the following:
                                    a. What’s the justification for the equation “ 4x  15  2x  3 ”?

                                                                   _______________________
                                    b. Find each of the following lengths:
               ST  ____ QT  ____ RT  ____ PT  ____
23. State whether the quadrilateral below is a quadrilateral. Justify
   your answer.




                             24. In the figure, JM KL . SHOW that the quadrilateral is a
                                 parallelogram for x  3 . Be sure to state which theorem is
                                 satisfied.




25. Complete the proof of Theorem 6-2-1 below:

   GIVEN: JKLM is a parallelogram
   PROVE: JK  LM , KL  MJ

                  Statement                                             Reason
1. JKLM is a parallelogram                         1. Given
2. JK   LM , KL MJ                                 2.
3. 1  2 , 3  4                               3.
4. JL  JL                                         4.
5. KJL  MLJ                                     5.
6. JK  LM , KL  MJ                               6. CPCTC

26. Fill in the blanks to complete the following sentence: “A _______________ is a

   parallelogram that has the properties of both a _______________ and a _______________.


27. RSTU is a rhombus, with mSRU  112 . Use it to answer the following:
   a. What justification is there for stating that mSRT  56 ?

                              ____________________
   b. Find mSUT .
                               mSUT  _____


                  28. In kite ABCD, mBCD  98 and mADE  47 . Find mABC .


                         mABC  _____
29. Use the figure at the right to do the following:
    a. Name the polygon by its side markings.
                                            _________________________
    b. Find the measures of each of the other angles.

                                        mJ  _____ mK  _____ mM  _____

                                   30. XY is the midsegment of trapezoid PQRS. Find XY.




31. A parallelogram has vertices A  2,1 , B  3, 2 ,
    C  4, 1 ,and D  3, 4  . Use diagonals to prove that
    the parallelogram is a rectangle. Clearly show what
    you do, as well as which theorem(s) you use. You do
    not have to graph the points, but you can if you want.
    [your best bet is to use distance formula to show the diagonals to be
    congruent]




32. Give the best name for the quadrilateral with vertices
     1,1 , 1,3  ,  3,1 , and 1, 3  . Show work to support
    your answer. Again, you don’t have to graph the
    points, but you can if you want.




                                          33. Three vertices of rectangle PQRS are P  3,2 , Q  1  ,
                                                                                                     ,4
                                               and R  8, 5  . Find the coordinates of vertex S. You may
                                               use the grid at the left to help you.
34. Write a two-column proof below:

     Given: ABCD is a kite
     Prove: ABE  CBE

                  Statement                                        Reason
1.                                              1.

2.                                              2.

3.                                              3.

4.                                              4.

5.                                              5.

6.                                              6.

7.                                              7.

8.                                              8.




The point breakdown on the test will be:
    10 points for #1
    1 point each for #2 through 16
    3 points for #17
    4 points each for #18 through 20 and 22 through 33
    6 points each for #21 and 34
    10 BONUS points

As usual, this PRACTICE TEST will be worth an additional 5 points, only under the following
conditions:
    It must be completed
    It must be corrected BEFORE I hand out the actual test; please do not wait until the
        beginning of the block to do this, plan ahead and come in before the block.

				
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