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Geometry Semester 2 Multiple Choice Final Review Answer Section 1. 2. 3. 4. 5. The triangles are congruent by SSS. 6. There is not enough information to determine whether the triangles are congruent by SSS or SAS. SAS does not apply because the congruent angles in the figure are not included angles. 7. The triangles are congruent by SAS. 8. There is not enough information to determine whether the triangles are congruent by SSS or SAS. SAS does not apply because the congruent angles in the figure are not included angles. 9. The triangles are congruent by AAS. 10. There is not enough information to determine whether the triangles are congruent by ASA or AAS. 11. The triangles are congruent by ASA. 12. by the Reflexive Property. 13. because they are vertical angles. using the SAS Triangle Congruence Theorem. using the ASA Triangle Congruence Theorem. 14. 15. 16. 17. 18. 19. B D A C Yes. There is enough information to conclude that by HA. No. might not be congruent to . There is not enough information. 20. Using and the Base Angle Theorem, . Using . Since and are supplementary, measures of the angles in a triangle is , . 21. cm. Using the Base Angle Converse Theorem, , where and . So, . and the Base Angle Theorem, . Since the sum of the . Solve the perimeter equation 22. Lake Winnie is 80 feet wide. The triangles are congruent by the Hypotenuse-Leg Congruence Theorem and corresponding parts of congruent triangles are congruent, so the width of Lake Winnie is equal to the length of the 48 meter leg of the triangle that is displayed below the lake. 23. Eight posts are needed to complete the fence. Using the Base Angle Converse Theorem, I know the length of side AC is equal to the length of side BC. She will need four more posts for side AC and four more posts for side BC. 24. 25. 26. The converse of the conditional would be: If a triangle is obtuse, then the measure of one of its angles is greater than . The converse is true. 27. The converse of the conditional would be: If a triangle is an isosceles triangle, then it has two sides with equal lengths. The converse is true. 28. The inverse of the conditional would be: If a polygon is not a triangle, then the sum of its exterior angles is not . The inverse is not true. 29. The inverse of the conditional would be: If a polygon is not a square, then it is not a rhombus. The inverse is not true. 30. The contrapositive of the conditional would be: If a quadrilateral is not a parallelogram, then it is not a rectangle. The contrapositive is true. 31. The contrapositive of the conditional would be: If the radius of a circle is not 6 inches, then the diameter of the circle is not 12 inches. The contrapositive is true. 32. 33. 34. The angle formed by the ramp and the ground is approximately 35. 36. 37. The angle formed by the string and the ground is approximately 38. 39. The angle formed by the rope and the dock is approximately 55.15 . 40. 41. 42. The area of the triangle is approximately 139.9 square centimeters. 43. The area of the triangle is approximately 10.6 square inches. 44. 45. 46. 47. 48. 49. 50. All rhombi have the properties of a parallelogram, so every rhombus must be a parallelogram. Penny is correct. 51. No. A rhombus has four congruent sides. If Sally makes the base of her sculpture with the four pieces of wood she has cut, all four sides of the quadrilateral will not be the same length. 52. The area of the kite is 75 square inches. 53. Each of the shorter sides is 14 centimeters. 54. The sum is equal to : The sum of the interior angles of the polygon is 55. The sum is equal to : The sum of the interior angles of the polygon is 56. 8 sides . . 57. 5 sides 58. The measure of each interior angle is . The measure of each interior angle is . 59. 60. The regular polygon has 5 sides. 61. The regular polygon has 18 sides. 62. 63. 64. Interior and exterior angles are supplementary. So subtract 65. Interior and exterior angles are supplementary. So subtract , the measure of the interior angle, from , the measure of the interior angle, from . . 66. 67. 68. 8 sides 69. 10 sides 70. rhombus parallelogram quadrilateral 71. rectangle parallelogram quadrilateral 72. kite quadrilateral 73. quadrilateral 74. False. Parallelograms have two pairs of parallel sides. Trapezoids only have one pair. 75. True 76. False. The diagonals of a rhombus, square, and a kite are perpendicular. 77. False. Both pairs of opposite angles are congruent in a parallelogram. 78. True. 79. False. All parallelograms have supplementary consecutive angles, not quadrilaterals. 80. point A 81. 82. 83. 84. point X 85. 86. 87. Sample answer: 88. Sample answer: 89. 90. 91. The measure of is . 92. 93. 94. 95. 96. The measure of arc FI is 120 degrees. 97. The measure of arc RS is 130 degrees. 98. 10 99. 5 100. 12 101. 102. 103. 104. 105. Fraction of C: Arc length of The arc length of is 3 meters. 106. Fraction of C: Arc length of The arc length of is cm. is cm. 107. Fraction of C: Arc length of The arc length of 108. Arc length: mm Perimeter of shaded region: 109. Arc length: mm cm Perimeter of figure: 110. Arc length: Perimeter of shaded region: 111. cm ft ft 112. 113. Arc length 114. Total area of the circle Sector AOB’s fraction of the circle Area of sector AOB The area of sector AOB is . 115. Total area of the circle Sector POQ’s fraction of the circle Area of sector POQ The area of sector POQ is . 116. Total area of the circle Sector AOB’s fraction of the circle Area of sector AOB Area of Area of the segment: The area of the shaded segment is approximately . 117. Because arc BCD is a semicircle, its measure is 118. 119. 120. . 121. 122. 123. center: ( 2, 2), radius: 5 124. This equation does not represent a circle because 125. center: (4, 5), radius: 6 126. The radius of circle B is , or 7. To calculate the circumference of B, substitute 7 for r in the formula for the circumference of a circle. A circle with three times the circumference of circle B has circumference 3(14 ), or 42 units. To calculate its radius, substitute 42 for C in the formula for the circumference of a circle, and then solve for r. The radius of the circle is 21. So an equation of the circle with the same center as circle B but with a circumference that is three times that of circle B is 127. Because the length of line segment AP is 8 units, line segment AP is a radius of circle A; therefore, point P must lie on circle A. 128. Because the length of line segment AP is 5 units, line segment AP is a radius of circle A; therefore, point P must lie on circle A. 129. 130.