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
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. mDAB mCBA 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
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
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 mJML 70 , which of the following is the
value of mJKM ?
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
a. 79° b. 101° c. 180° d. 360°
16. In trapezoid PQRS, which of the following is the length of midsegment
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 mD .
c. What’s the justification for the equation “ 16x 2 12y 10 180 ”?
d. Find the value of 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
24. In the figure, JM KL . SHOW that the quadrilateral is a
parallelogram for x 3 . Be sure to state which theorem is
25. Complete the proof of Theorem 6-2-1 below:
GIVEN: JKLM is a parallelogram
PROVE: JK LM , KL MJ
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 mSRU 112 . Use it to answer the following:
a. What justification is there for stating that mSRT 56 ?
b. Find mSUT .
28. In kite ABCD, mBCD 98 and mADE 47 . Find mABC .
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.
mJ _____ mK _____ mM _____
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
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 ,
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
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
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.