<p> CP Geometry Midterm Review Packet Name:______Date:______</p><p>True or False:</p><p>1.______Every line segment has one and only one midpoint.</p><p>2. ______If two angles are equal, they are right angles.</p><p>3. ______If two angles are supplementary, then they are equal.</p><p>4. ______Two points determine one and only one plane.</p><p>5. ______An angle has one and only one bisector.</p><p>6. ______The sum of two acute angles is an obtuse angle.</p><p>7. ______If a triangle is equilateral, then it is isosceles.</p><p>8. ______Since the sum of 20°, 30°and 40° is 90°, then the angles are complementary.</p><p>9. ______Every polygon has more than three sides.</p><p>10. ______The sum of the interior and exterior angles of a pentagon are the same.</p><p>Set up and solve the following word problems.</p><p>11. Two angles are supplementary. Find the angles if one angle is 45°more than twice the other angle.</p><p>12. Two angles are complimentary. If one angle is 32° less than the other, Find the angles. 13. Two angles are supplementary. Find the angles if one angle is 10°more than two- thirds the other angle.</p><p>14. In a triangle, <B is 12° larger than <A. <C is equal to the sum of the first two angles. Find the angles.</p><p>15. ΔABC is isosceles and one of the base angles is 15° larger than the vertex angle. Find the angles. </p><p>16. In a triangle, <B is 2 times as large as <A. If <C is 4° less than <A, find all three angles.</p><p>17. Find the sum of the interior angles of a heptagon.</p><p>18. Find the number of degrees in each exterior angle of a regular octagon.</p><p>19. How many sides does a polygon have if the sum of its interior angles is 1800°?</p><p>20. How many sides does a regular polygon have if each interior angle is 144°? Solve the following angle problems:</p><p>21. A < BED = 52°</p><p>B < CED = 28° < AEB = 18° Find < AEC______</p><p>C</p><p>E D</p><p>22. EB bisects < AED A < AED = 74° B < BEC = 19° Find < CED______</p><p>C</p><p>E D</p><p>23. < AEB = 29° 14’ A < CED = 31° 26’ B < BEC = 24° 34’ Find < AED______</p><p>C</p><p>E D 24. A BC bisects < ABD < ABD = 71° 38’ C Find < CBD______</p><p>B D</p><p>25. (BE Bisects < ABC) < ABD = 56° < DBC = 28° Find < ABE______</p><p>A < E</p><p>D </p><p>B C</p><p>26. A < ABE = 83° 14’ C < ABC = 23° 48’ < CBD = 27° 17’ Find < DBE = ______D</p><p>B E 27. ∆ABC is isosceles with base AC. m< A = 3xm< B = 4x Find x = ______m< A= ______m< B = _____ m< C=_____ B</p><p>A C</p><p>28. ΔABC is isosceles with base AC. m< BCD = 110° Find m< A ______m< B ______m< ACB______B</p><p>A C D</p><p>Draw the segment and then solve.</p><p>29. B is the midpoint of AC . AC = _____ AB = _____ AC = x + 3 BC = _____ AB = x</p><p>AC = _____ AB = _____ BC = _____ 30. B is between points A and C. AB = 4x – 1 BC = 2x + 3 AC = 8x 31. Find the sum of the measures of the interior angles of a 11-gon.</p><p>______</p><p>32. The measure of each exterior angle of a polygon is 45o. Find the number of sides of the polygon.</p><p>______</p><p>33. Find the measures of an interior and exterior angle of a regular pentadecagon.</p><p>______</p><p>34. The measure of an interior angle of a regular polygon is 120o. Find the number of sides of the polygon.</p><p>______</p><p>35. If the exterior angle of a regular polygon measures 36o, find the sum of the measures of the interior angles.</p><p>______36. If the measure of each of the interior angles of a regular polygon is 100 more than the measure of each of the exterior angles, name the polygon.</p><p>______37. The sum of the interior angles of a polygon are 900o. Name the polygon.</p><p>______</p><p>38. The measures of the interior angles of a pentagon are x, 3x, 2x – 1, 6x – 5, and 4x + 2. Find the measure of each angle.</p><p>39. Δ DOG ≈ Δ ______BY:______</p><p>C D</p><p>A O G T</p><p>40. Δ BID ≈ Δ______BY:______I</p><p>B D R</p><p>41. Δ SAN ≈ Δ______BY:______</p><p>S N</p><p>A</p><p>E K</p><p>42. Δ GTA ≈ Δ______BY:______</p><p>G</p><p>O</p><p>T</p><p>A 43. Δ ABD ≈ Δ______BY:______Given < ADB ≈ < CDB A</p><p>B D</p><p>C</p><p>44. Δ ABC ≈ Δ______BY:______D</p><p>A C</p><p>E</p><p>B</p><p>Use the following sketch to solve: C</p><p>A B D</p><p>E F H</p><p>G</p><p>45. < ABF = 6x – 16 < BFH = 2x +28 Find X ______< EFB______< CBD______46. < DBF = 5x + 16 < BFH = 3x + 12 Find X______< ABF______< EFB______</p><p>Solve: 47. If two lines are parallel and are cut by a transversal, two alternate interior angles represented by 3x and 5x – 70. Find the angle measures.</p><p>48. If two lines are parallel and are cut by a transversal, two corresponding Angles represented by 2x + 10 and 4x -50. Find the angle measures.</p><p>49. If two lines are parallel and are cut by a transversal, two same side interior angles represented by 2x and 3x. Find the angle measures.</p><p>Use the following sketch for # 50 – 55. A E G</p><p>7 5 8 F 6</p><p>3 B 1 4 2 C D H</p><p>50. List all Alternate Interior angles.______</p><p>51. List all Alternate Exterior angles.______</p><p>52. List all Corresponding angles.______</p><p>53. List all Same side interior angles.______</p><p>54. If < ABC = 108° then < GFH =______; < HFB=______</p><p>55. If < DBF = 95°, then < BFH=______; < BFE=______A B I 56. </p><p>C D E</p><p>F G H</p><p>ABP CE P FH �ABD 32 �BDG 89 �EDG ______�DGH ______</p><p>E</p><p>57. A F B 5x+16 ABP CD �BFG ______C G 3x+12 D �FGD ______</p><p>H</p><p>E</p><p>A F B 58. AB || CD 6x - 16 <AFG = ______</p><p><FGD = ______2x +28 C G D</p><p>A E H</p><p>B G F</p><p>C D 59. BF || CD EC bisects <ACD <EGF = 42° < CBF = ______< ABG = ______</p><p>Simplify each radical expression</p><p>17 60. 4 600 61. 62. 4 96  2 54 3</p><p>Set up the following ratio and reduce to lowest terms.</p><p>63. 10 inches to 3 feet ______</p><p>64. 30 minutes to 5 hours ______</p><p>65. 5 3 to 27 ______</p><p>Solve the proportion.</p><p>7 9 4 3 2 66.  67.  x 27 3 x 16 x 7 5 x 68.  69.  x 4 2 5 8 5</p><p>Are the triangles similar? If so, write a similarity statement and identify the postulate or theorem that justifies your answer.</p><p>70. A D G 92° 68°</p><p>23° C T 92° O</p><p>10 71. S L N</p><p>8 15 20 6</p><p>M A B 25</p><p>72. B Z 24 Y 32° 12 44</p><p>A 9 C 32°</p><p>X</p><p>Use the given information to determine the similar triangles. Then, solve for the missing side.</p><p>73. Given AG YM. Y RA = 5 A AG = 6 YM = 15 Find RM = ____</p><p>R</p><p>G M</p><p>74. Given AB DE. A B AB = 2 5 AC = 4 3 C ED = 5 6 Find CD = ______</p><p>D E 75. Find x and y in the diagram below if EB DC.</p><p>D DC = 27 AD = 33 E AB = 20 AC = 30 x Find x = _____ y Find y = _____ A</p><p>B C</p><p>76. If ABC ~ QPR , m < A = 30° and m < B = 97°, find the measures of angles Q, P, and R.</p><p> m < Q = _____ m < P = ______m < R = ______</p><p>77.-79 Use the diagram at the right to the answer the next 3 questions. 77. If AB=3x+8 and GJ=2x+24, what is AB? ______</p><p>78. If AC=3y-5 and HJ=4y+2, what is HB? ______</p><p>79. If GH=7z-1 and BC=4z-3, what is GH? ______80-83. Is this triangle possible? 9. 2.5, 3.5, 5 ______10. 2, 6, 9 ______11. 9, 12, 15 ______</p><p>84-85. Find the third side. Write an inequality statement.</p><p>84. 5, 15, ______85. 8, 22, ______</p><p>86-87 Find the missing angles. 86. 87.</p><p>88-91 Use the diagram to the right. 88. If AB=BC, and m B=75, then the longest side is ______. 89. If m A=90, then the longest side is ______.</p><p>90. If AB=8, BC=6 and AC=13, then the largest angle is ______.</p><p>91. If AB=5, BC=7, and AC=10, then the smallest angle is ______.</p>