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Geometry 300 Midterm Review Name_________________________ Date_____________________ 1. In the figure shown, HG IJ , IH 5, FJ 24, and JG 4. Find FI . H I F J G 2. In ACE, BD AE , AE 56, DE 12, CD x, and BD 14. Find CE. C B D A 3. The supplement of an angle is ten more than double the complement. Define the variables and find the angle, complement and supplement. 4. The ratio of the measures of the angles of a quadrilateral is 3:7:11:15. What is the measure of each angle in the quadrilateral? 5. The measures of the sides of an isosceles trapezoid are in the ratio of 5.5 : 4 : 5.5 : 10. If the perimeter of the trapezoid is 300 feet, then what is the length of the median of the trapezoid? E Geometry 300 Midterm Review Name_________________________ Date_____________________ 6. Give 4 different ways to name the angle to the right. Define the following terms: 7. right angle 8. straight angle 9. obtuse angle 10. acute angle 11. linear pair 12. Find the complement and supplement of 52 . 13. Find the complement and supplement of 103 . 14. In the diagram at the right, name 3 collinear points. 15. In the diagram at the right, name 3 noncollinear points. 16. Given square ABCD with the diagonals intersecting at point E. Find mDBA . Geometry 300 Midterm Review Name_________________________ Date_____________________ 17. In rectangle OPQR, the diagonals intersect at point S. If OS = 12, then find OQ + PR. 18. The bases of a trapezoid are (9x + 3) and (13x + 1). If the median is (12x - 4), find the value of x. 19. WV is a base of isosceles trapezoid TUVW. If mW 3x 6 and mV 5x 28 , then find the value of x. 20. In parallelogram ABCD, mA 4 x 8 and mD 13x 18 . Find mC . 21. In rectangle JKLM, the diagonals intersect at point N. If JN x 2 2 x and KM 4x 24 , then find the value(s) of x that make this problem work and find the length(s) of JL . Geometry 300 Midterm Review Name_________________________ Date_____________________ In problems 22-27, determine whether the triangles are congruent (use SSS, SAS, ASA or AAS). If they are congruent, write the postulate that proves they are congruent. If they are not congruent, write “NC.” 22. 23. 24. 25. 26. 27. 28. In rectangle ABCD, the diagonals AC and BD intersect in point E. If AE = 2x + 3 and BE = 12 – x, find BD. A. B. C. D. 3 9 18 None of the above. Geometry 300 Midterm Review Name_________________________ Date_____________________ 29. In rectangle ABCD, the diagonals AC and BD intersect in point E. If mBAC 3x 5 and mACD 40 2 x , find mAED . A. B. C. D. 52 7 26 None of the above. 30. In square ABCD the diagonals intersect at E, mDAC y and mBAC 3x . Find x. A. B. C. D. 15 30 60 None of the above. For problems 31 and 32, list ALL the names that apply to a quadrilateral with the given vertices. Then circle the name that BEST applies. Show mathematical proof of your answer (this means slopes and distances). 31. E(0, -3), F(-3, 0), G(0, 3), H(3, 0) 32. P(1, 3), Q(-3, -1), R(-2, -8), S(8, 2) Geometry 300 Midterm Review Name_________________________ Date_____________________ 33. Given parallelogram PQRS with P = 7x and Q = 8x + 30, find the measures of R and S . Use parallelogram ABCD and the given information to find each value. 34. AC = 5x – 12 and AT = 14. Find x. 35. BC = 4x + 7 and AD = 8x – 5. Find x. 36. m<BCD = 3x + 14 and m<ADC = x + 10. Find m<ADC. Geometry 300 Midterm Review Name_________________________ Date_____________________ 37. If quadrilateral BLUE is a rectangle, find the value of x. b) EB = x2 - 10, UL = x + 20 a) LP = 7x - 3, UB = 78 38. ABC is equilateral, AB = 1 x 8 and BC 3x 3 . Find x, AC , and find the 2 perimeter of the triangle. 39. Find the value of x, mA and mB. A B 4x + 20o 40o C 40. Given DEF with mD (7b 1) o , mE (2b 1) o and mF (b 8) o . Find b, mE and classify the triangle by its angles. Geometry 300 Midterm Review Name_________________________ Date_____________________ 41. Find y and mJHK . G H (14y – 14)o (6y)o (7y – 3)o K J 42. Determine the value of x in the diagram. 77o xo 154o 43. In the diagram, a // b . Find the m1. 70o 44. In the diagram, a // b . Find the m2 a 15o 35o b 2 1 45. In the diagram, a // b and c // d . Find the m3 . 3 a 40o b c d 95o a b Geometry 300 Midterm Review Name_________________________ Date_____________________ 46. In LMN , the measure of the largest angle is 32 less than 3 times the smallest angle. The measure of the middle angle is 8 more than half the measure of the largest angle. Draw and label a diagram. Use your knowledge of Geometry and Algebra to determine the measure of the middle angle. 3 o 5 y , mS y o , 2 2 mSQR ( x 2 5x 66) o and mPQS 100 o . Find the values of x, y and the measures of S and R . 47. In the diagram, QRS is acute, mR R S Q P 48. In the diagram below, a || b , m6 115 and m2 70 . Find m3 . Geometry 300 Midterm Review Name_________________________ Date_____________________ 49. Using the diagram below (which is not necessarily drawn to scale), if m3 66 x 2 and m 2 (12 x 21) , find the value(s) of x, then find all reasonable values for m8 . 50. Find the values of x and y. 51. Find the values of x, y and z. 52. Find the values of x, y and z. Geometry 300 Midterm Review Name_________________________ Date_____________________ 53. M and N are vertical angles. Are M and N right angles if mM 4 x 14 and mN 6 x 24 ? Use the diagram at right. If the stated information is true, name the lines which would be parallel. If no lines would be parallel, write “none.” 54. 13 8 ______________ 56. 6 2 ______________ 57. 2 7 ______________ 58. 8 9 ______________ 59. 7 15 ______________ 60. 1 9 ______________ 61. 10 11 ______________ 62. 4 10 180 ______________ 63. Given point A(-20, 13) and point B(-24, 60), do the following: a) find the length AB to the nearest hundredth, b) find the coordinates of the midpoint of AB using the MIDPOINT FORMULA. Geometry 300 Midterm Review Name_________________________ Date_____________________ 64. An obtuse angle has a measure of (15x + 15). What is the range of possible values for x? 65. The sum of three times an angle and four times its complement exceeds twice its supplement by 15. Find the measure of the angle, its complement and its supplement. 66. Determine the possible values of x. Use the value(s) of x that make sense for this problem to find the measures of the four angles. 67. Find the value of x, y and mFCD if mF 10 x 8 y 14 mFCB 4 x 5 y 2 mFBC 3x 5 y 36 Geometry 300 Midterm Review Name_________________________ Date_____________________ True or False: 68. _____ An angle can be named by its vertex. 69. _____ A line contains two planes. 70. _____ If A, B, and C are distinct point on a line, then AB + BC = AC. 71. _____ A midpoint must be positive. 72. _____ If line k lies in plane M, then the intersection of the line k and plane M is a point. Always – Sometimes – Never (write A, S or N) 73. _____ If a ray divides an angle into two acute angles, then that ray bisects the angle. 74. _____ If two angles are adjacent and congruent, then they are vertical angles. 75. _____ If two intersecting lines form congruent adjacent angles, then the lines are perpendicular. 76. _____ If two angles are supplementary, then they are a linear pair. 77. ____ If two angles are supplementary and congruent, then they are right angles. 78. EF has endpoint E(3, 7) and midpoint M(-4, 6). Find the coordinates of endpoint B. 79. In the figure at right CX bisects AB at X and CD bisects XB at Y. Given the following conditions, find the value of x and the measure of the indicated segment. a. AX = 2x + 11, XB = 4x – 5; find AB b. AB = x + 3, AX = 3x – 1; find XB Geometry 300 Midterm Review Name_________________________ Date_____________________ 80. In the figure at the right, TE bisects GTM and TO bisects ETM. mOTM = 7x – 5 and mGTE = 15x-17. Find mGTO. 81. Using the diagram at the right, name a segment that is skew to AB . 82. Using the diagram at the right, name a segment that is parallel to AB . 83. Using the diagram at the right, name a plane parallel to plane FBC. 84. Are the following points collinear? Use algebra to prove your conclusion. A(-5, 9), B(-1, 1), C(1, -4) 85. In the diagram, r t. Find m3.