Math Geometry Semester 1 Review Answer Key

Semester 1 Exam – Review Honors Geometry Name:___________________________ Hour: _______ Answer the following questions. Show ALL work. 1. If  ABC   BAC, then  ABC is: a. isosceles b. equilateral c. scalene d. obtuse e. nonexistent 2. Find the angle formed by the hands of a clock at 10:30. 3. Find the range of possible values for x below: 6 4. The measures of two complementary angles are in the ratio of 4:11. Find the measure of the supplement of the smaller angle. x 8 For 5-7 on the right, use the drawing belowIt is given that ABCD is a square with a side of length 6: 5. Find the coordinates of D Y (2,4) A 6. Find the exact area of the circle B 7. If point A is reflected over the horizontal axis, find the coordinates of this reflected point X C D For 8-10, give a reason for each of the conclusions: 8. 9. B A 10. A C A V F D 1 3 2 4 V C Given:  DCA is comp to  BCA  BCA is comp to  BAC Conclusion:  DCA   BAC Given: CF & VF are angle bisectors  VCA   AVC Conclusion:  1   4 Conclusion: AV  AV 8. ___________________________ 9. __________________ Page 2 of 12 10. ________________ For 11-21, find the value of X: 11. 12. A 13. X B 14. 4 100° X 3 2 75° C x 130° D E X° 93° 9 Given: ABCDE is a reg. pent. 11. ________ 12. _______ 13. ________ 14. _______ 15. 16. 17. 18. 6 7.4 X 9 6 1321726 X X X 4 X 6 8 6 15. ___________ 16. _______ 19. 17. ________ 20. 18. _______ 21. x 50° 5 X 1 2 3 10 3 130° 4 5 X 19. ___________ Given:  ’s 1-5  20. ________ 22. Given: ABC is inscribed to a circle at the points (-7,0), (11,-6), (13,0). Is ABC a right triangle? 23. C 21. _________ O U x2 3x+54 72-3x R T A C OTR is obtuse CTU is acute TO bisects CTU Can UTR be a right angle? Justify. B Page 3 of 12 For 24-28, choose the most descriptive answer. A. parallelogram B. kite C. rectangle D. square E. rhombus ____24. If one diagonal of a quadrilateral bisects a pair of opposite angles, the quadrilateral is a __. ____ 25. If the consecutive sides of a rhombus are joined by their midpoints, the figure formed is a ___. ____ 26.If the figure would be a square except that it has oblique (non-  ) diagonals, it must be a __. ____ 27. If opposite sides have equal slopes, the figure is a ____. ____ 28.If each diagonal divides the figure into two congruent isosceles triangles,then the figure is a_. For 29 - 37, choose the best answer: ____ 29. AB is a segment in plane m, and XY is a perpendicular bisector of AB . Which must be true? a. XY m b. XY  m c. If P is on XY , then PA  PB d. If PA  PB , then P is on XY ____ 30. The supplement of an angle is 6 times the complement of the angle. Find the supplement. a. 70 b. 72 c. 8 d. 108 e. no supplement exists ____ 31. An angle is 4 times as great as its supplement. Find the measure of the complement of the angle. a. 36 b. 54 c. 72 d. 144 e. none ____ 32. Find the measure of each interior angle of an octagon. a. 45 b. 60 c. 120 d. 135 e. insufficient information given ____ 33. Two sides of a  have lengths 6 & 8. Which of the following could not be the length of the 3rd side? a. 2 b. 13 c. 8 d. 8.25 e. all are possible sides ____ 34. The supplement of the complement of an angle is 132. What is the supplement of the angle? a. 42 b. 31 c. 138 d. 222 e. no supplement exists ____ 35. TRAM is a rhombus. Which of the following is not necessarily true? T 3 2 R 5 a. m  5 = 90 b.  2   3 c.  2   4 d.  5 >  4 e. All of the above are true 4 M A ____ 36. Solve for x 30° _____ 37. a. 46 70-3x° 2 3 b. 1 3 c. 0 d. 70 e. impossible 40° Given: DCE  BAE Which of the following is not necessarily true? A B a. AD is parallel to BC b. AB is parallel to DC E c. AC bisects BD d. E is the midpoint of AC e. a – d are true D C Page 4 of 12 38. The measure of two consecutive angles of a parallelogram have a ratio of 11:1. Find the measure of the larger angle. 39. List all of the ways it could be proven that 40.The hour hand of a clock stopped, but the minute hand continued to move for 155 PSQ  PSR P minutes. How many degrees would the hour hand have moved if it had not gotten stuck? Q R S For 41-42, use the drawing on the left: P 41. What is PQR  RQS ? ______________ 42. What is QR  QS ? ________________ R Q S For 43-44, use the drawing on the left: H 43. Given: The perimeter of HJK is 42, J  HKJ and HJ:JK = 3:4. Find JK = ________ 44. Given: HJ = HK, m HKL = x + 50 and m H = x - 30 Find m H = ____________ K J L For 45-46, use the drawing on the left: 45. Find the midpoint of BC ___________ A (0,8) 46. Find the slope of the median to BC C (6,0) ____________ B (-8,-6) 47. Find the measure of 1 _______ 48. Find the measure of 3 ________ 3 1 125 142° 49. Given: PRSQ is a quadrilateral Plane m is parallel to Plane n PQ is contained to Plane m 50. Given: ABC  DEF, DF = 10, AB = 18 Perimeter of ABC = 40 Find DE + EF _____________ RS is contained to Plane n PR is parallel to QS mQSR  5x  6 & mPRS  x  12 , mPQS  ________ Page 5 of 12 For 51-65, write A for always, S for sometimes, or N for never ____ 51. If two angles are supplementary and congruent, they are right angles. ____ 52. The diagonals of a trapezoid bisect each other. ____ 53. If a triangle is equilateral, then it is equiangular. ____ 54. If a quadrilateral is equilateral, then it is equiangular. ____ 55. Definitions are reversible. ____ 56. In space, if two lines are parallel to the same line, then they are parallel to each other. ____ 57. A rhombus is a kite ____ 58. The perpendicular bisector of the base of an isosceles triangle bisects the vertex angle ____ 59. If a line is perpendicular to a plane, it is perpendicular to a line in that plane ____ 60. The measure of an exterior angle of a triangle is greater than every interior angle of the triangle. ____ 61. If the diags of a quadrilateral bisect each other & bisect the angles, the quadrilateral is a square. ____ 62. The median to the hypotenuse of a right triangle + average of the legs = half the triangle’s perimeter. ____ 63. The sum of the diagonals of a rectangle is equal to the perimeter ____ 64. The sum of the complements of the three angles of a triangle is 90 65. The sum of the measures of the angles 66. The sum of an angle plus its complement plus of a regular polygon is 2880. its supplement is 200 more than the angle. Find the measure of each angle. Find the measure of the supplement of the angle. ________ ____________ 67. Name the polygon that has 54 diagonals. 68. A right triangle is determined by the x-axis, y-axis, and a line. If the line crosses the x-axis at (-7, 0), and the slope of the line is 2 , find 5 the point where the line crosses the y- axis. _____________________ ______________ 69. Given that the shape below is trapezoid, find y: 70. Given: TP is parallel to RA , RA = 16 20° TP = 25, TE bisects RTP, PE bisects TPA Find the perimeter of TRAP R A E 35° 55° y T 69. _______________ P 70. _________________ Page 6 of 12 For 71, use the following vertices for ABC : A = (3,1) B = (-7,4) C = (-3,10) 71. a. Find the slope of the median from A to BC b. Find the slope of the altitude from A to BC a. _________ b. _________ 72. Given: SPQR is an isosceles trapezoid m S = x + 40 m Q = 2x – 7 73. The sum of an angle and four times its complement is 20 greater than the supplement of the angle. Find the angle’s complement. 72. Find: m R = _______ 73. ______________ 74. 75. 3 X x 4 16 3 13 15 74. X = ____________ 75. 76. a. Find the fourth proportional in a proportion whose first 3 terms are 5, 3 and 30. X = _________ 77. The sum of the angles of an equiangular polygon is 3960 . Find the measure of each exterior angle. b. Find the mean proportionals between 8 & 18 76. a. _________________ b. _______________ 78. 79. A 4 C 77. ____________ A x x+2 12 D B B E Given: BC is the base of isosceles ABC DE is the base of isosceles AED mBAE  40 78. Find CB = ____________ 79. Page 7 of 12 Find mDEC  _____ C 80. 81. A A D D E E C B C B Given: mA  120 BD & BE trisect ABC CD & CE trisect ACB Given: BD & BE trisect ABC DE = 4, EC = 5, BD = 12 Find mD  _____& mE  ________ Find BC = _____& BE = ____ & AD = _____ 82. Points (1,3), (-4, 7) and (-29, k) are collinear. Find k. 82. k = _________ 83. A pair of consecutive angles of a parallelogram are in the ratio 5 : 3. Find the measure of the smaller angle. 83. ___________ For 84-86, use the drawing on the left: T 84. Find RM _______ 85. Find AM _______ 10 86. Find TA ________ R 6 A M For 87-89, use the drawing on the left: A 87. Given that mA = 40, mB = 3x + 10 and mACD = 7x-30, Find x _________ 88. Given that mA = 4x, mB = x + 45 and mACD = 8x-15, Find mACB = _______ B C D 89. In #87, is CAB isosceles? _______ In #88? _______ 90. The perimeter of an isosceles triangle is 36. One side is 10. What are the possible lengths of the base? 91. Find the number of sides of an equiangular polygon if each interior angle is 170 . 90. _______________ 91. n = ___________ Page 8 of 12 For 92-96, use the drawing on the left, given that all three polygons are regular: 92. Find m1  _____ 93. Find m2  _____ 1 4 3 94. Find m3  _____ 95. Find m4  _____ 5 96. Find m5  _____ 2 97. Given: GRAM is a parallelogram A 98. M 35° 25° 40° X 150° 110° R G X 97. X = ________ 98. X = ________ 99. Find the sum of the measures of the angles of a nonagon. 99. _____________ 100. If each angle of a regular polygon is 168 , how many sides does it have? 100. _____________ 101. How many diagonals does a heptagon have? 101. ____________ 102. Find the mean proportionals between ¼ and 49. 102. ____________ 103. Solve 5 10  for y. 5  y y  10 103. ____________ 104. A woman walks 20 m west, 100 m south, another 8 m west and then 4 m north. How far is she from her starting point? 104. ____________ Page 9 of 12 S Use the following drawing for 105-106: T R P 105. Given: PS = 15, RS = 12, RQ = 6 PQ = 16 Q 106. Given: T and R are midpoints SR = 2, ST = 4, TR = 6 PT = __________ TR = __________ Find the perimeter of Quad PTRQ = _________ 107. 108. Find the measure of each angle. 30° y° x2 – 19x° 102° z° 80 – 2x° 50° 107. y = __________ z = __________ 108. ____________ 109. Find the restrictions on x for AMV to be a triangle: *Hint* Triangle Inequality & __________ 110. R 20 A X–1 3X – 5 T X 30 M V C O X+4 Given: COT  ROU Find X 109. _______________________________ 110. X = ____________ For 111-120, choose the best answer: ____111. 1 2 M Given: AMV  AVM 1  3 Then 2  4 by: a. the Subtraction Property b. the Addition Property c. the Transitive Property d. the Division Property A 3 4 V Page 10 of 12 U ____ 112. Four angles of a pentagon each have measure of 100 . The fifth angle measures: a. 150 b. 140 c. 120 d. 108 e. 100 ____ 113. Given: In ABC & DEF , AB  FE , AC  DF & A  F . Which of the following are true? a. ABC  DEF b. ABC  DFE c. ABC  FED d. ABC  EDF e. All of these ____ 114. A quadrilateral must be a parallelogram if: a. a diagonal separates the quadrilateral into two congruent triangles. c. the diagonals are perpendicular b. the diagonals are congruent d. the diagonals are bisectors of each other. e. it has four sides. ____ 115. Five angles have measures 135,110,20,91 & 100. If 3 angles are selected at random, find the probability that all three are obtuse. a. 3 5 b. 4 5 c. 2 5 d. 2 3 e. 9 10 ____ 116. Find x in the following rectangle. x 40° a. 45 c. 70 b. 20 d. 60 ____ 117. Two opposite angles of an isosceles trapezoid are: a. congruent b. complementary c. supplementary d. vertical e. not necessarily any of these ____ 118. The diagonals are perpendicular and congruent in a(n): a. rectangleb. kite c. rhombus d. square e. isosceles trapezoid ____ 119. Which of the following statements is NOT always true? a. The diagonals of a rectangle are  b. The diagonals of a rhombus are perpendicular bisectors c. The diagonals of an isosceles trapezoid are  d. The diagonals of a parallelogram bisect their angles e. All of the above are true. ____ 120. If diagonals of a parallelogram are congruent, the parallelogram must be a(n): a. square b. rhombus c. rectangle d. isosceles trapezoid Page 11 of 12 e. kite ANSWERS 1. a 2. 135 3. 2 < x < 14 4. 156 5. (8, -2) 6. 9  7. (2, -4) 31. E 32. E 33. A 34. C 35. E 36. C 37. E 8. 2 angles are comp. 38. 165 61. S 62. A 63. N 64. S 65. 160 66. 145 67. Dodecagon 4 68. 2 5 91. 36 92. 60 93. 135 94. 120 95. 45 96. 105 97. 65 69. 40 99. 1260 100. 30 98. 95 to the same angle 39. SAS, SSS 9. Division ASA, AAS, HL 10. Reflexive 40. 77.5 70. 57 11. 72 41. QR 71. a.  12. 130 42. RQS 72. 89 OR 91 43. 16.8 73. 10 14. 92 44. 20 74. 15. 2351 17 45. (-1, -3) 75. 12 105. 5 & 16. 7.4 17. 12 18. 5 46. 11 47. 35 48. 128 76. a. 18 b. 12 77. 15 78. 20 19. 100 49. 41 79. 20 20. 9 50. 30 80. 140 & 160 106. 24 107. 108 & 130 108. 150, 30 OR 92, 88 10 109. < x< 8 3 110. 80 21. 36 51. A 81. 15 & 4 10 & 4 111. A 22. Yes 23. Yes 52. N 53. A 112. B 113. C 24. B 54. S 25. C 55. A 26. E 27. A 28. E 29. C 30. D 56. A 57. A 58. A 59. S 60. S 82. 27 83. 67.5 2 84. 16 3 2 85. 10 3 86. 8 87. 20 88. 35 89. Yes, No 90. 10 or 16 13. 27 4 2 3 ; b.  4 3 16 5 Page 12 of 12 101. 14 7 2 2 103. 6 3 102.  104. 100m 114. D 115. C 116. B 117. C 118. D 119. D 120. C 32 3