Geometry hapter 5 Review Sheet Name: 1. List the 6 properties of the parallelogram. 2. List the 5 ways to prove that a quadrilateral is a parallelogram. 3. Name two properties of the rectangle that are not properties of the parallelogram in general. 4. Name three properties of the rhombus that are not properties of the parallelogram in general. 5. Name 5 properties of the square that are not properties of the parallelogram in general. 6. How does a trapezoid differ from a parallelogram? 7. What is the definition of an isosceles trapezoid? 8. Name two properties of the isosceles trapezoid that are not properties of the trapezoid in general. 9. What is the definition of the median of a trapezoid? 10. What is the definition of the midline of a triangle? True/alse 11. very square is a rectangle. 12. The median of a trapezoid is the segment joining the midpoints of the bases. 13. The base angles of a trapezoid are congruent. 14. parallelogram with two consecutive sides congruent is a rhombus. 15. The diagonals of a trapezoid bisect each other. 16. If the diagonals of quadrilateral are perpendicular, then the quadrilateral is a rhombus. 17. There exists a trapezoid with three congruent sides. 18. If 2 pairs of consecutive angles of a quadrilateral are supplementary, then the quadrilateral is a parallelogram. 19. ll quadrilaterals are either parallelograms or trapezoids. 20. If the midlines of equilateral triangle are drawn to form triangle WY, then triangle WY is an equiangular triangle. 21. quadrilateral that is both a rectangle and a rhombus is a square. 22. If the diagonals of a trapezoid are congruent then the trapezoid is isosceles. 23. There exists a rhombus that is a rectangle. 24. If two consecutive sides of a quadrilateral are congruent, then the quadrilateral is a rhombus. 25. quadrilateral with one right angle is a rectangle. Write the theorem of definition that justifies why quadrilateral is a parallelogram. If not enough information is given, write INS. 26. ; 27. ; 28. ; 29. 30. supp ; supp
Solve each of the following. Given quadrilateral GH is a parallelogram. 31. If 3, then G 32. If m H 115, then m G 33. If G, then m 34. If m HG 70, then m G 35. If G, and H 8, then G H G 36. If G, and m HG 42, then m HG 37. If GH 22, then 38. If quad. GH is a square, then m HG 39. If m G 38,and m HG 78, then m G 40. If H 22( x 6) and G 10(2x 3), then x Solve each of the following. Given:, is the midpoint of, is the midpoint of 41. If 12, then 42. If 4x 8 and x 10, then Y 43. If and Y are midpoints of and, respectively, and Y 10, then Solve each of the following. Given: trapezoid ( ) with median. 44. If 12, then 18 then = 45. If 2x 4, 3x 5, and x 9, then x 46. If, m 72, then () m and ( ) m 47. If, 3x 2 and 2x 6, then x
Prove each of the following. 48. G: Quadrilateral is a parallelogram; P: 49. G: Quadrilateral is a parallelogram; 1 2; ; P: Quadrilateral is a parallelogram 1 2 50. G: Trapezoid ; ; P:
What type of quadrilateral is it? ( The diagonals of quad WYZ intersect at ) 51. W Y YZ WZ 52. W ZY; WZ Y; WY Z 53. W Y; Z 54. ZW YW ; W YZ; WY Z 55. WZ Y; W ZY 56. W ZY; WZ Y; m ZW 90 ; W Y 57. WZ W ; WZ Y 58. WY Z; WY Z 59. W YZ; WY Z 60. WZ Y; WZ Y; WZ YZ
Geometry hapter 5 Review Sheet nswers 1 10. See Notes 11. True 12. alse 13. alse 14. True 15. alse 16. alse 17. True 18. alse 19. alse 20. True 21. True 22. True 23. True 24. alse 25. alse 26. If the diagonals of a quad bisect each other, Then the quad is a parallelogram 27. INS 28. If the both pairs of opposite angles of a quad are congruent, then the quad is a parallelogram 29. INS 30. INS 31. 3 32. 65 33. 90 34. 70 35. 16 36. 48 37. 22 38. 45 39. 40 40. 81 41. 24 42. 32 43. 40 44. 6 45. 5 46. 72 ; 108 47. 8 48. See below 49. See below 50. See below 51. rhombus 52. rectangle 53. parallelogram 54. rhombus 55. parallelogram 56. square 57. See below 58. none 59. See below 60. rhombus 48. 1., 1. Given are 2. 2. Opposite side of a. 3. 3. efinition of a 4. 4. lines that alt. int. 's are 5. 5. SS 6. 6. PT 49. 1. ; 1 2; 1. Given 2. 2. Opposite side of a are 3. 3. S 4. 4. PT 5. is a parallelogram 5. If one pair of opposite sides of a quad. are both then the quad. is a parallelogram. & parallel, 50. 1. Trapezoid ; ; 1. Given 2. is an isosceles trapezoid 2. efinition of isosceles trapezoid 3. 3. iagonals of isosceles trapezoid are congruent. 4. 4. Reflexive Property 5. 5. SSS 6. 6. PT 7. 7. Vertical angles are congruent. 8. 8. S 9. 9. PT 57. trapezoid if W is not parallel to ZY or rhombus if W ZY 59. isosceles trapezoid if WZ is not parallel to Y or rectangle if WZ Y