Name Date Class. 6. In JKLM, what is the value of m K? A 15 B 57 A RS QT C QR ST
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1 Name Date Class CHAPTER 6 Chapter Review #1 Form B Circle the best answer. 1. Which best describes the figure? 6. In JKLM, what is the value of m K? A regular convex heptagon B irregular convex heptagon C irregular concave heptagon D irregular convex hexagon 2. What is the measure of each interior angle in a regular convex nonagon? A 40 B What is the value of a? C 180 D 1260 A 15 B 57 C 65 D QR ST. Which additional information is NOT enough to conclude that QRST is a parallelogram? A RS QT C QR ST B RS QT D Q S 8. Which of the quadrilaterals MUST be parallelograms? A 2 C 180 B 90 D Not here 4. The diagonals of ABCD intersect at X. Which is always true? A BX XD B AX XB C A D D m A m C In DEFG, what is EG? A 25 C 50 B 30 D Not here A A only B B only 9. Which is NOT always true? C Neither A nor B D Both A and B A The diagonals of a rectangle divide the rectangle into four nonoverlapping isosceles triangles. B The diagonals of a square divide the square into four nonoverlapping right triangles. C The longer diagonal of a rhombus is perpendicular to two sides of the rhombus. D The sum of the lengths of the diagonals of a rhombus is less than the perimeter of the rhombus. 1 Holt Geometry
2 Name Date Class CHAPTER 6 Chapter Review Form B continued 10. WXYZ is a rectangle. Which is NOT an expression for WT? 14. In kite UVWX, m XUV 84, and m WVX 68. What is m VWX? A 5x 18 C 10x 12 B 7x 6 D 12x Which set of numbers could be the measures of DAB, ACB, and DBC, respectively? A 22 B 42 C 44 D GE 5x 2 and DF 8x 7. What is GE? A 114, 57, 32.5 B 115, 32.5, 57.5 C 116, 57.5, 32.5 D 117, 58.5, What additional information would allow you to conclude that JKLM is a rhombus? A 16 B 17 C 18 D In trapezoid PQRS, if YX is the midsegment, what could be the lengths of PQ and SR? A JK ML and JM KL. B JM JK C JL and MK bisect each other. D JL MK 13. Which is the best name for the quadrilateral with vertices at (2, 2), (5, 2), (1, 5), and ( 2, 1)? A parallelogram C rhombus B rectangle D square A 4 cm and 8 cm B 9 cm and 15 cm C 17 cm and 31 cm D 18 m and 30 m 2 Holt Geometry
3 17.24 cm in or about in 2 Performance Assessment 1. Perpendicular Bisector Theorem 2. B is the midpoint of AC since BE is a midsegment ; Def. of perpendicular bisector 4. BDC, DBE, EDB, ABE, A 5. AE AB; AEB 90, ABE 45, and, if two angles in a triangle are not congruent, then the longer side is opposite the larger angle. 6. The triangles are not congruent. The reasoning in the answer for question 5 can be used to show that AB AE and AB EB and likewise that DC BC. But since AB BC, it follows that DC is longer than each side of ABE. Therefore ABE cannot be congruent to CDB. 7. a. 14 b. 14 2, or about 19.8 c. 28 d. 28 2, or about 39.6 Cumulative Test 1. C 20. H 2. F 21. C 3. D 22. G 4. H 23. A 5. A 24. H 6. G 25. B 7. A 26. F 8. J 27. D 9. D 28. H 12. F 31. B 13. D 32. H 14. G 33. A 15. A 34. H 16. G 35. C 17. D 36. G 18. F 37. B 19. D 38. G CHAPTER 6 Section Quiz: Lessons 6-1 Through D 6. F 2. H 7. B 3. D 8. J 4. H 9. B 5. A Section Quiz: Lessons 6-4 Through A 6. G 2. J 7. D 3. A 8. J 4. J 9. A 5. A Chapter Test Form A: Multiple Choice 1. D 9. C 2. C 10. A 3. A 11. A 4. D 12. B 5. A 13. B 6. A 14. A 7. B 15. A 8. A 16. A 10. G 29. B 11. C 30. J 261 Holt Geometry
4 Chapter Test Form B: Multiple Choice 1. C 9. C 2. G 10. J 3. A 11. D 4. F 12. G 5. C 13. D 6. H 14. H 7. B 15. B 8. J 16. H Chapter Test Form C: Multiple Choice 1. C 9. D 2. G 10. H 3. D 11. B 4. F 12. F 5. D 13. B 6. G 14. J 7. C 15. A 8. J 16. F Chapter Test Form A: Free Response 1. True False True 8. Find JM and KL. JM 5x 1 and KL 3x 5 Given JM 5(3) 1 14 Subst. and simplify. KL 3(3) 5 14 Subst. and simplify. Since JM KL and JM KL, JKLM is a parallelogram by Theorem True Sample answer: True 13. valid Chapter Test Form B: Free Response 1. irregular hexagon A quadrilateral is a parallelogram if and only if it has two pairs of parallel sides. 5. AB 30; BX True 8. m J (9y 1) [9(14) 1] 127 ; m L (10y 13) [10(14) 13] 127 ; m K (7x 4) [7(7) 4] 53 ; Since , K is supplementary to both J and L. JKLM is a parallelogram by Theorem square; rhombus; rectangle in Not valid; possible answer: conditions for a rectangle are 1 of a g is a rt. or the diagonals of a g are. While the quadrilateral is a g and a rhombus, neither of the conditions for a rectangle are met. 262 Holt Geometry
5 13. Sample answer: DF EG [2 ( 5)] + (1 0) [1 ( 4)] [( 2) 3] 5 ( 5) The diagonals are congruent so by Theorem 6-5-2, DEFG is a rectangle. DF ( 5) EG 1 1 ( 4) 5 1 (1) 1, so DF is not perpendicular 7 to EG. So DEFG is not a rhombus and therefore cannot be a square. DEFG is a rectangle Chapter Test Form C: Free Response 1. irregular, concave hexagon sides ( 4, 0) or It is given that KJL MLJ, so by the Converse of the Alternate Interior Angles Theorem, JK LM. It is also given that JK LM. Since one pair of opposite sides are both and parallel, JKLM is a parallelogram AB 2 4 ( 2) CD AD 4 ( 4) BC 6 ( 2) 8 2 Since both pairs of opposite sides are parallel (same slope), ABCD is a parallelogram by definition. 9. rectangle True 13. rectangle 14. kite or Performance Assessment 1. a.parallelogram; Both pairs of opposite sides are congruent, and the figure does not appear to be either a rhombus or rectangle. b. x 5 c a. kite; Exactly two pairs of adjacent sides are congruent, and all four sides are not congruent. b. x 10 c a. BD AC ; If the diagonals of a parallelogram are congruent, then it is a rectangle. b. AD CD (or AD AB ); All sides are congruent and all angles are right angles. c. yes; All sides of a rhombus are equal in length, so the perimeter is 4(38), or Holt Geometry
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