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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. 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 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 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 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 mD . mD _____ 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 mSRU 112 . Use it to answer the following: a. What justification is there for stating that mSRT 56 ? ____________________ b. Find mSUT . mSUT _____ 28. In kite ABCD, mBCD 98 and mADE 47 . Find mABC . 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 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.