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GEOM. FINAL EXAM REVIEW PACKAGE Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ 1. ____ two points are collinear. a. Any b. Sometimes 2. How are the two angles related? c. No 52° 128° Drawing not to scale ____ a. vertical c. complementary b. supplementary d. adjacent 3. Each unit on the map represents 5 miles. What is the actual distance from Oceanfront to Seaside? y 8 6 Seaside 4 2 –8 –6 –4 –2 –2 Landview –4 2 4 6 8 x Oceanfront –6 –8 ____ a. 10 miles b. 50 miles 4. Which statement is true? a. are same-side angles. c. about 8 miles d. about 40 miles ____ b. are same-side angles. c. are alternate interior angles. d. are alternate interior angles. 5. The Polygon Angle-Sum Theorem states: The sum of the measures of the angles of an n-gon is ____. a. b. c. d. ____ 6. Complete this statement. The sum of the measures of the exterior angles of an n-gon, one at each vertex, is ____. a. (n – 2)180 b. 360 c. d. 180n ____ 7. What must be true about the slopes of two perpendicular lines, neither of which is vertical? a. The slopes are equal. b. The slopes have product 1. c. The slopes have product –1. d. One of the slopes must be 0. 8. Based on the given information, what can you conclude, and why? Given: ____ I K J H L a. by ASA c. by ASA b. by SAS d. by SAS ____ 9. Where can the bisectors of the angles of an obtuse triangle intersect? I. inside the triangle II. on the triangle III. outside the triangle a. I only b. III only c. I or III only d. I, II, or II ____ 10. Name the smallest angle of The diagram is not to scale. C 5 A 6 7 B a. b. c. Two angles are the same size and smaller than the third. ____ 11. ____ 12. ____ 13. ____ 14. d. Which three lengths could be the lengths of the sides of a triangle? a. 12 cm, 5 cm, 17 cm c. 9 cm, 22 cm, 11 cm b. 10 cm, 15 cm, 24 cm d. 21 cm, 7 cm, 6 cm Two sides of a triangle have lengths 10 and 18. Which inequalities describe the values that possible lengths for the third side? a. c. x > 10 and x < 18 b. x > 8 and x < 28 d. Which statement is true? a. All quadrilaterals are rectangles. b. All quadrilaterals are squares. c. All rectangles are quadrilaterals. d. All quadrilaterals are parallelograms. What is the missing reason in the proof? Given: parallelogram ABCD with diagonal Prove: A D B C Statements 1. 2. 3. 4. 5. 6. a. Reflexive Property of Congruence b. ASA Reasons 1. Definition of parallelogram 2. Alternate Interior Angles Theorem 3. Definition of parallelogram 4. Alternate Interior Angles Theorem 5. Reflexive Property of Congruence 6. ? c. Alternate Interior Angles Theorem d. SSS Short Answer 15. Are O, N, and P collinear? If so, name the line on which they lie. O N P M 16. If scale. and then what is the measure of The diagram is not to 17. Name an angle supplementary to 18. Find the circumference of the circle in terms of . 39 in. 19. Write this statement as a conditional in if-then form: All triangles have three sides. 20. What is the converse of the following conditional? If a point is in the first quadrant, then its coordinates are positive. 21. When a conditional and its converse are true, you can combine them as a true ____. 22. Name the Property of Equality that justifies the statement: If p = q, then . 23. Name the Property of Congruence that justifies the statement: If . 24. . Find the value of x for p to be parallel to q. The diagram is not to scale. 3 4 5 1 2 6 p q 25. Find the value of k. The diagram is not to scale. 62° k° 45° 26. Find the values of x, y, and z. The diagram is not to scale. 38° 19° 56° x° z° y° 27. Find the value of the variable. The diagram is not to scale. 114° x° 47° 28. Find the missing angle measures. The diagram is not to scale. 125° x° 124° y° 65° 29. Use the information given in the diagram. Tell why A and B D C 30. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to scale. d° 38° g 5 b f° e° 52° 3 c 31. Justify the last two steps of the proof. Given: and Prove: R S T U Proof: 1. 2. 3. 4. 4 1. Given 2. Given 3. 4. 32. From the information in the diagram, can you prove ? Explain. 33. What is the measure of a base angle of an isosceles triangle if the vertex angle measures 38° and the two congruent sides each measure 21 units? 38° 21 21 Drawing not to scale 34. Find the value of x. The diagram is not to scale. | | S (3 x – 50)° R (7 x )° T U 35. Find the value of x. The diagram is not to scale. 40 x 40 32 25 25 36. Use the information in the diagram to determine the height of the tree. The diagram is not to scale. 150 ft 37. Q is equidistant from the sides of Find the value of x. The diagram is not to scale. T | | | 4)° 2 + x (2 30° | Q R S 38. bisects Find FG. The diagram is not to scale. E n +8 F ) 3n – 4 ) D G 39. Name a median for | A E ) | D ) C F B 40. For a triangle, list the respective names of the points of concurrency of • perpendicular bisectors of the sides • bisectors of the angles • medians • lines containing the altitudes. 41. What is the name of the segment inside the large triangle? 42. ABCD is a parallelogram. If then The diagram is not to scale. A B D C 43. For the parallelogram, if scale. and 3 find The diagram is not to 4 2 1 44. In the parallelogram, and J Find The diagram is not to scale. K O M L | | 45. In the rhombus, The diagram is not to scale. 3 1 | | 2 46. Find the values of a and b.The diagram is not to scale. Find the value of each variable. a° 113° 36° b° 47. The Sears Tower in Chicago is 1450 feet high. A model of the tower is 24 inches tall. What is the ratio of the height of the model to the height of the actual Sears Tower? 48. If then 3a = ____. Solve the proportion. 49. 50. Solve the extended proportion for x and y with x > 0 and y > 0. 51. An artist’s canvas forms a golden rectangle. The longer side of the canvas is 33 inches. How long is the shorter side? Round your answer to the nearest tenth of an inch. 52. Are the triangles similar? If so, explain why. 30.4° 84.6° 84.6° 65° State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. 53. 54. Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not to scale. 55. Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale. 5 26 56. Given: . Find the length of . The diagram is not drawn to scale. A 6 P Q 12 18 B C Find the value of x. Round your answer to the nearest tenth. 57. 7 x Not drawn to scale 58. is tangent to circle O at B. Find the length of the radius r for AB = 5 and AO = 8.6. Round to the nearest tenth if necessary. The diagram is not to scale. B A r O 59. Find the perimeter of the rectangle. The drawing is not to scale. 47 ft 57 ft Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x. (Figures are not drawn to scale.) 60. 111 x° O Find the length of the missing side. The triangle is not drawn to scale. 61. 6 8 Find the value of x to the nearest degree. 62. 58 3 x 63. Write the ratios for sin A and cos A. A 5 4 C B 3 Not drawn to scale 64. A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts a 249-foot-long shadow. Find the measure of to the nearest degree. 100 ft A 249 ft 65. The area of a square garden is 50 m2. How long is the diagonal? The polygons are similar, but not necessarily drawn to scale. Find the values of x and y. 66. Triangles ABC and DEF are similar. Find the lengths of AB and EF. A D 5x 5 E B 4 x F C 67. Write the tangent ratios for and . P 29 21 R Q 20 Not drawn to scale 68. In triangle ABC, is a right angle and leave it in simplest radical form. 45. Find BC. If you answer is not an integer, C 11 ft B A Not drawn to scale 69. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain. 70. If to scale. find the values of x, EF, and FG. The drawing is not E F G 71. Find AC. A B C D –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 72. Which point is the midpoint of A B C –8 –7 –6 –5 –4 –3 –2 –1 73. bisects not to scale. , ? D 0 1 E 2 3 4 5 6 7 , 8 . Find . The diagram is Find the length of the missing side. Leave your answer in simplest radical form. 74. 8m 7m Not drawn to scale 75. Name the ray in the figure. A B Solve for x. 76. > 3x 4x 3x + 7 > > 5x – 8 77. Name a fourth point in plane TUW. 78. Find the value of x. (7x – 8)° (6x + 11)° Drawing not to scale 79. Line r is parallel to line t. Find m 5. The diagram is not to scale. r 7 135° 1 3 t 4 2 5 6 80. In the figure, the horizontal lines are parallel and scale. M A 3 L K J B C D Find JM. The diagram is not to GEOM. FINAL EXAM REVIEW PACKAGE Answer Section MULTIPLE CHOICE 1. ANS: A PTS: 1 DIF: L2 REF: 1-3 Points, Lines, and Planes OBJ: 1-3.1 Basic Terms of Geometry NAT: NAEP 2005 G1c | ADP K.1.1 STA: MA G.G.1b TOP: 1-4 Example 1 KEY: point | collinear points | reasoning 2. ANS: B PTS: 1 DIF: L2 REF: 1-6 Measuring Angles OBJ: 1-6.2 Identifying Angle Pairs NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3g STA: MA G.G.6 TOP: 1-6 Example 4 KEY: supplementary angles 3. ANS: D PTS: 1 DIF: L3 REF: 1-8 The Coordinate Plane OBJ: 1-8.1 Finding Distance on the Coordinate Plane NAT: NAEP 2005 M1e | ADP J.1.6 | ADP K.10.3 STA: MA G.G.12 KEY: coordinate plane | Distance Formula | word problem | problem solving 4. ANS: D PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel Lines OBJ: 3-1.1 Identifying Angles NAT: NAEP 2005 M1f | ADP K.2.1 STA: MA G.G.2 | MA G.G.2b TOP: 3-1 Example 1 KEY: same-side interior angles | alternate interior angles 5. ANS: D PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle Sums NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.6 | MA G.G.7 KEY: Polygon Angle-Sum Theorem 6. ANS: B PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle Sums NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.6 | MA G.G.7 KEY: Polygon Exterior Angle-Sum Theorem 7. ANS: C PTS: 1 DIF: L2 REF: 3-7 Slopes of Parallel and Perpendicular Lines OBJ: 3-7.2 Slope and Perpendicular Lines NAT: NAEP 2005 A1h | NAEP 2005 A2a | ADP J.4.1 | ADP J.4.2 | ADP K.10.2 STA: MA G.G.6 | MA G.G.11 | MA G.G.11a | MA G.G.11b | MA G.G.11c | MA G.G.12 | MA G.G.13 KEY: slopes of perpendicular lines | perpendicular lines | reasoning 8. ANS: A PTS: 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS OBJ: 4-3.1 Using the ASA Postulate and the AAS Theorem NAT: NAEP 2005 G2e | ADP K.3 STA: MA G.G.2 | MA G.G.2b | MA G.G.6 TOP: 4-3 Example 4 KEY: ASA | reasoning 9. ANS: A PTS: 1 DIF: L3 REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.1 Properties of Bisectors NAT: NAEP 2005 G3b STA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.12 KEY: incenter of the triangle | angle bisector | reasoning 10. ANS: D PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles OBJ: 5-5.1 Inequalities Involving Angles of Triangles NAT: NAEP 2005 G3f STA: MA G.G.2 | MA G.G.2b | MA G.G.10 TOP: 5-5 Example 2 KEY: Theorem 5-10 11. ANS: B PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles OBJ: 5-5.2 Inequalities Involving Sides of Triangles NAT: NAEP 2005 G3f STA: MA G.G.2 | MA G.G.2b | MA G.G.10 TOP: 5-5 Example 4 KEY: Triangle Inequality Theorem 12. ANS: B PTS: 1 DIF: L2 REF: 5-5 Inequalities in Triangles OBJ: 5-5.2 Inequalities Involving Sides of Triangles NAT: NAEP 2005 G3f STA: MA G.G.2 | MA G.G.2b | MA G.G.10 TOP: 5-5 Example 5 KEY: Triangle Inequality Theorem 13. ANS: C PTS: 1 DIF: L2 REF: 6-1 Classifying Quadrilaterals OBJ: 6-1.1 Classifying Special Quadrilaterals NAT: NAEP 2005 G3f STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.11 | MA G.G.11a | MA G.G.12 KEY: reasoning | kite | parallelogram | quadrilateral | rectangle | rhombus | special quadrilaterals 14. ANS: B PTS: 1 DIF: L3 REF: 6-2 Properties of Parallelograms OBJ: 6-2.2 Properties: Diagonals and Transversals NAT: NAEP 2005 G3f STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 KEY: proof | two-column proof | parallelogram | diagonal SHORT ANSWER 15. ANS: No, the three points are not collinear. PTS: 1 DIF: L2 REF: 1-3 Points, Lines, and Planes OBJ: 1-3.1 Basic Terms of Geometry NAT: NAEP 2005 G1c | ADP K.1.1 STA: MA G.G.2b TOP: 1-4 Example 1 KEY: point | line | collinear points 16. ANS: 20 PTS: 1 DIF: L2 REF: 1-6 Measuring Angles OBJ: 1-6.1 Finding Angle Measures NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3g STA: MA G.G.6 TOP: 1-6 Example 3 KEY: Angle Addition Postulate 17. ANS: PTS: 1 DIF: L2 REF: 1-6 Measuring Angles OBJ: 1-6.2 Identifying Angle Pairs NAT: NAEP 2005 M1e | NAEP 2005 M1f | NAEP 2005 G3g STA: MA G.G.6 TOP: 1-6 Example 4 KEY: supplementary angles 18. ANS: 78 in. PTS: 1 DIF: L2 REF: 1-9 Perimeter, Circumference, and Area OBJ: 1-9.1 Finding Perimeter and Circumference NAT: NAEP 2005 M1c | NAEP 2005 M1h | ADP I.4.1 | ADP J.1.6 | ADP K.8.1 | ADP K.8.2 STA: MA G.G.1 | MA G.G.12 | MA G.M.1 TOP: 1-9 Example 2 KEY: circle | circumference 19. ANS: If a figure is a triangle, then it has three sides. PTS: 1 DIF: L2 REF: 2-1 Conditional Statements OBJ: 2-1.1 Conditional Statements NAT: NAEP 2005 G5a STA: MA G.G.2b | MA G.G.2c TOP: 2-1 Example 2 KEY: hypothesis | conclusion | conditional statement 20. ANS: If the coordinates of a point are positive, then the point is in the first quadrant. PTS: 1 DIF: L2 REF: 2-1 Conditional Statements OBJ: 2-1.2 Converses NAT: NAEP 2005 G5a STA: MA G.G.2b | MA G.G.2c TOP: 2-1 Example 5 KEY: conditional statement | coverse of a conditional 21. ANS: biconditional PTS: 1 DIF: L2 REF: 2-2 Biconditionals and Definitions OBJ: 2-2.1 Writing Biconditionals NAT: NAEP 2005 G1c | NAEP 2005 G5a | ADP K.1.1 STA: MA G.G.2b | MA G.G.2c TOP: 2-2 Example 1 KEY: conditional statement | biconditional statement 22. ANS: Subtraction Property PTS: 1 DIF: L2 REF: 2-4 Reasoning in Algebra OBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry NAT: NAEP 2005 A2e | NAEP 2005 G5a | ADP J.3.1 STA: MA G.G.2b | MA G.G.2c | MA G.G.5 | MA G.G.6 TOP: 2-4 Example 3 KEY: Properties of Equality 23. ANS: Symmetric Property PTS: 1 DIF: L2 REF: 2-4 Reasoning in Algebra OBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry NAT: NAEP 2005 A2e | NAEP 2005 G5a | ADP J.3.1 STA: MA G.G.2b | MA G.G.2c | MA G.G.5 | MA G.G.6 KEY: Properties of Congruence 24. ANS: 20 PTS: OBJ: NAT: STA: KEY: 25. ANS: 73 TOP: 2-4 Example 3 1 DIF: L2 REF: 3-3 Parallel and Perpendicular Lines 3-3.1 Relating Parallel and Perpendicular Lines NAEP 2005 M1e | NAEP 2005 M1f | ADP K.2.1 MA G.G.2 | MA G.G.2b | MA G.G.5 TOP: 3-3 Example 2 parallel lines PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle AngleSum Theorem OBJ: 3-4.1 Finding Angle Measures in Triangles NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 3-4 Example 1 KEY: triangle | sum of angles of a triangle 26. ANS: PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle AngleSum Theorem OBJ: 3-4.1 Finding Angle Measures in Triangles NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 STA: MA G.G.1 | MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7 TOP: 3-4 Example 1 KEY: triangle | sum of angles of a triangle 27. ANS: 19 PTS: 1 DIF: L3 REF: 3-4 Parallel Lines and the Triangle AngleSum Theorem OBJ: 3-4.1 Finding Angle Measures in Triangles NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 STA: MA G.G.1 | MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7 KEY: triangle | sum of angles of a triangle | vertical angles 28. ANS: x = 114, y = 56 PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems OBJ: 3-5.2 Polygon Angle Sums NAT: NAEP 2005 G3b | NAEP 2005 G3f | ADP J.5.1 | ADP K.1.2 STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.6 | MA G.G.7 TOP: 3-5 Example 4 KEY: exterior angle | Polygon Angle-Sum Theorem 29. ANS: Reflexive Property, Given PTS: 1 DIF: L2 REF: 4-1 Congruent Figures OBJ: 4-1.1 Congruent Figures NAT: NAEP 2005 G2e | ADP K.3 STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 4-1 Example 4 KEY: congruent figures | corresponding parts | proof 30. ANS: 3 PTS: 1 DIF: L2 REF: 4-1 Congruent Figures OBJ: 4-1.1 Congruent Figures NAT: NAEP 2005 G2e | ADP K.3 STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 4-1 Example 1 KEY: congruent figures | corresponding parts 31. ANS: Reflexive Property of ; SSS PTS: 1 DIF: L2 REF: 4-2 Triangle Congruence by SSS and SAS OBJ: 4-2.1 Using the SSS and SAS Postulates NAT: NAEP 2005 G2e | ADP K.3 STA: MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 4-2 Example 1 KEY: SSS | reflexive property | proof 32. ANS: yes, by ASA PTS: OBJ: K.3 STA: KEY: 33. ANS: 71° 1 DIF: L2 REF: 4-3 Triangle Congruence by ASA and AAS 4-3.1 Using the ASA Postulate and the AAS Theorem NAT: NAEP 2005 G2e | ADP MA G.G.2 | MA G.G.2b | MA G.G.6 ASA | reasoning TOP: 4-3 Example 3 PTS: 1 DIF: L2 REF: 4-5 Isosceles and Equilateral Triangles OBJ: 4-5.1 The Isosceles Triangle Theorems NAT: NAEP 2005 G3f | ADP J.5.1 | ADP K.3 STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7 | MA G.G.8 TOP: 4-5 Example 2 KEY: isosceles triangle | Converse of Isosceles Triangle Theorem | Triangle Angle-Sum Theorem 34. ANS: PTS: 1 DIF: L3 REF: 4-5 Isosceles and Equilateral Triangles OBJ: 4-5.1 The Isosceles Triangle Theorems NAT: NAEP 2005 G3f | ADP J.5.1 | ADP K.3 STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7 | MA G.G.8 TOP: 4-5 Example 2 KEY: Isosceles Triangle Theorem | isosceles triangle 35. ANS: 64 PTS: OBJ: K.1.2 STA: KEY: 36. ANS: 75 ft 1 DIF: L2 REF: 5-1 Midsegments of Triangles 5-1.1 Using Properties of Midsegments NAT: NAEP 2005 G3f | ADP PTS: OBJ: K.1.2 STA: TOP: KEY: 37. ANS: 3 1 DIF: L2 REF: 5-1 Midsegments of Triangles 5-1.1 Using Properties of Midsegments NAT: NAEP 2005 G3f | ADP PTS: OBJ: K.2.2 STA: KEY: 38. ANS: 14 1 DIF: L2 REF: 5-2 Bisectors in Triangles 5-2.1 Perpendicular Bisectors and Angle Bisectors NAT: NAEP 2005 G3b | ADP PTS: OBJ: K.2.2 STA: KEY: 39. ANS: 1 DIF: L2 REF: 5-2 Bisectors in Triangles 5-2.1 Perpendicular Bisectors and Angle Bisectors NAT: NAEP 2005 G3b | ADP MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 midsegment | Triangle Midsegment Theorem TOP: 5-1 Example 1 MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.3 | MA G.G.5 | MA G.G.6 5-1 Example 3 midsegment | Triangle Midsegment Theorem | problem solving MA G.G.2b | MA G.G.5 | MA G.G.6 angle bisector | Converse of the Angle Bisector Theorem MA G.G.2b | MA G.G.5 | MA G.G.6 angle bisector | Angle Bisector Theorem TOP: 5-2 Example 2 TOP: 5-2 Example 2 PTS: 1 DIF: L2 REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.2 Medians and Altitudes NAT: NAEP 2005 G3b STA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.12 TOP: 5-3 Example 4 KEY: median of a triangle 40. ANS: circumcenter incenter centroid orthocenter PTS: 1 DIF: L3 REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.2 Medians and Altitudes NAT: NAEP 2005 G3b STA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.12 KEY: angle bisector | circumcenter of the triangle | centroid | orthocenter of the triangle | median | altitude | perpendicular bisector 41. ANS: midsegment PTS: 1 DIF: L2 REF: 5-3 Concurrent Lines, Medians, and Altitudes OBJ: 5-3.2 Medians and Altitudes NAT: NAEP 2005 G3b STA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.12 TOP: 5-3 Example 4 KEY: altitude of a triangle | angle bisector | perpendicular bisector | midsegment | median of a triangle 42. ANS: 115 PTS: OBJ: STA: KEY: 43. ANS: 163 1 DIF: L2 REF: 6-2 Properties of Parallelograms 6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3f MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 parallelogram | opposite angles | Theorem 6-2 PTS: OBJ: STA: TOP: KEY: 44. ANS: 129 1 DIF: L3 REF: 6-2 Properties of Parallelograms 6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3f MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 6-2 Example 2 algebra | parallelogram | opposite angles | consectutive angles | Theorem 6-2 PTS: 1 DIF: L3 REF: 6-2 Properties of Parallelograms OBJ: 6-2.1 Properties: Sides and Angles NAT: NAEP 2005 G3f STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 KEY: parallelogram | opposite angles 45. ANS: x = 6, y = 84, z = 10 PTS: OBJ: STA: TOP: 46. ANS: 1 DIF: L2 REF: 6-4 Special Parallelograms 6-4.1 Diagonals of Rhombuses and Rectangles NAT: NAEP 2005 G3f MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 6-4 Example 1 KEY: algebra | diagonal | rhombus | Theorem 6-13 PTS: 1 DIF: L2 REF: 6-5 Trapezoids and Kites OBJ: 6-5.1 Properties of Trapezoids and Kites NAT: NAEP 2005 G3f STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.2c | MA G.G.5 | MA G.G.6 | MA G.G.7 TOP: 6-5 Example 1 KEY: trapezoid | base angles | Theorem 6-15 47. ANS: 1 : 725 PTS: OBJ: NAT: STA: 1 DIF: L2 REF: 7-1 Ratios and Proportions 7-1.1 Using Ratios and Proportions NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7 MA G.G.2b | MA G.M.5 TOP: 7-1 Example 1 KEY: ratio | word problem 48. ANS: 5b PTS: OBJ: NAT: STA: KEY: 49. ANS: 9 1 DIF: L2 REF: 7-1 Ratios and Proportions 7-1.1 Using Ratios and Proportions NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7 MA G.G.2b | MA G.M.5 TOP: 7-1 Example 2 proportion | Cross-Product Property PTS: 1 DIF: L2 REF: 7-1 Ratios and Proportions OBJ: 7-1.1 Using Ratios and Proportions NAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7 STA: MA G.G.2b | MA G.M.5 TOP: 7-1 Example 3 KEY: proportion | Cross-Product Property 50. ANS: x = 3; y = 12 PTS: 1 DIF: L4 REF: 7-1 Ratios and Proportions OBJ: 7-1.1 Using Ratios and Proportions NAT: NAEP 2005 NAEP 2005 N4c | ADP I.1.2 | ADP J.5.1 | ADP K.7 STA: MA G.G.2b | MA G.M.5 TOP: 7-1 Example 4 KEY: extended proportion | Cross-Product Property 51. ANS: 20.4 in. PTS: 1 DIF: L2 REF: 7-2 Similar Polygons OBJ: 7-2.2 Applying Similar Polygons NAT: NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7 STA: MA G.G.2b | MA G.G.5 TOP: 7-2 Example 5 KEY: similar polygons 52. ANS: yes, by AA PTS: 1 DIF: L2 REF: 7-3 Proving Triangles Similar OBJ: 7-3.1 The AA Postulate and the SAS and SSS Theorems NAT: NAEP 2005 G2e | ADP I.1.2 | ADP K.3 STA: MA G.G.2 | MA G.G.2b | MA G.G.5 TOP: 7-3 Example 2 KEY: Angle-Angle Similarity Postulate | Side-Side-Side Similarity Theorem | Side-Angle-Side Similarity Theorem 53. ANS: ; SAS PTS: OBJ: NAT: STA: KEY: 1 DIF: L2 REF: 7-3 Proving Triangles Similar 7-3.1 The AA Postulate and the SAS and SSS Theorems NAEP 2005 G2e | ADP I.1.2 | ADP K.3 MA G.G.2 | MA G.G.2b | MA G.G.5 TOP: 7-3 Example 2 Side-Angle-Side Similarity Theorem | corresponding sides 54. ANS: 42.3 m PTS: OBJ: NAT: STA: KEY: 55. ANS: 130 1 DIF: L2 REF: 7-3 Proving Triangles Similar 7-3.2 Applying AA, SAS, and SSS Similarity NAEP 2005 G2e | ADP I.1.2 | ADP K.3 MA G.G.2 | MA G.G.2b | MA G.G.5 TOP: 7-3 Example 4 Side-Angle-Side Similarity Theorem | word problem PTS: OBJ: NAT: STA: TOP: 56. ANS: 9 1 DIF: L2 REF: 7-4 Similarity in Right Triangles 7-4.1 Using Similarity in Right Triangles NAEP 2005 G2e | ADP I.1.2 | ADP K.3 MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 7-4 Example 2 KEY: corollaries of the geometric mean | proportion PTS: OBJ: NAT: STA: KEY: 57. ANS: 4 1 DIF: L2 REF: 7-5 Proportions in Triangles 7-5.1 Using the Side-Splitter Theorem NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 7-5 Example 1 Side-Splitter Theorem PTS: OBJ: NAT: STA: KEY: 58. ANS: 7 1 DIF: L2 REF: 8-3 The Tangent Ratio 8-3.1 Using Tangents in Triangles NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2 MA G.G.6 | MA G.G.9 TOP: 8-3 Example 2 side length using tangent | tangent | tangent ratio PTS: 1 DIF: L2 REF: 12-1 Tangent Lines OBJ: 12-1.1 Using the Radius-Tangent Relationship NAT: NAEP 2005 G3e | ADP K.4 STA: MA G.G.2b | MA G.G.5 | MA G.G.6 | MA G.G.7 TOP: 12-1 Example 3 KEY: tangent to a circle | point of tangency | properties of tangents | right triangle | Pythagorean Theorem 59. ANS: 208 feet PTS: OBJ: NAT: STA: 60. ANS: 69 1 DIF: L2 REF: 1-9 Perimeter, Circumference, and Area 1-9.1 Finding Perimeter and Circumference NAEP 2005 M1c | NAEP 2005 M1h | ADP I.4.1 | ADP J.1.6 | ADP K.8.1 | ADP K.8.2 MA G.G.12 TOP: 1-9 Example 1 KEY: perimeter | rectangle PTS: OBJ: K.4 STA: KEY: 61. ANS: 10 1 DIF: L2 REF: 12-1 Tangent Lines 12-1.1 Using the Radius-Tangent Relationship NAT: NAEP 2005 G3e | ADP MA G.G.16 TOP: 12-1 Example 1 tangent to a circle | point of tangency | properties of tangents | central angle PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: 8-1.1 The Pythagorean Theorem NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3 STA: MA G.G.2b | MA G.G.5 TOP: 8-1 Example 1 KEY: Pythagorean Theorem | leg | hypotenuse 62. ANS: 22 PTS: OBJ: NAT: STA: KEY: 63. ANS: 1 DIF: L3 REF: 8-3 The Tangent Ratio 8-3.1 Using Tangents in Triangles NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2 MA G.G.6 | MA G.G.9 TOP: 8-3 Example 3 inverse of tangent | tangent | tangent ratio | angle measure using tangent PTS: OBJ: NAT: STA: KEY: 64. ANS: 22 1 DIF: L2 REF: 8-4 Sine and Cosine Ratios 8-4.1 Using Sine and Cosine in Triangles NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2 MA G.G.6 | MA G.G.9 TOP: 8-4 Example 1 sine | cosine | sine ratio | cosine ratio PTS: 1 DIF: L3 REF: 8-3 The Tangent Ratio OBJ: 8-3.1 Using Tangents in Triangles NAT: NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2 STA: MA G.G.6 | MA G.G.9 TOP: 8-3 Example 3 KEY: angle measure using tangent | word problem | problem solving | tangent | inverse of tangent | tangent ratio 65. ANS: 10 m PTS: 1 DIF: L2 REF: 8-2 Special Right Triangles OBJ: 8-2.1 45°-45°-90° Triangles NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.5.1 | ADP K.5 STA: MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.7 | MA G.G.8 | MA G.G.10 TOP: 8-2 Example 3 KEY: special right triangles | diagonal 66. ANS: AB = 10; EF = 2 PTS: OBJ: NAT: STA: KEY: 67. ANS: 1 DIF: L2 REF: 7-2 Similar Polygons 7-2.1 Similar Polygons NAEP 2005 G2e | NAEP 2005 M1k | ADP I.1.2 | ADP J.5.1 | ADP K.7 MA G.G.2b | MA G.G.5 TOP: 7-2 Example 3 corresponding sides | proportion | similar polygons PTS: OBJ: NAT: STA: TOP: KEY: 68. ANS: 11 1 DIF: L2 REF: 8-3 The Tangent Ratio 8-3.1 Using Tangents in Triangles NAEP 2005 M1m | ADP I.1.2 | ADP I.4.1 | ADP K.11.1 | ADP K.11.2 MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.7 | MA G.G.8 | MA G.G.10 8-3 Example 1 tangent ratio | tangent | leg opposite angle | leg adjacent to angle ft PTS: 1 DIF: L3 REF: 8-2 Special Right Triangles OBJ: 8-2.1 45°-45°-90° Triangles NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.5.1 | ADP K.5 STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.7 | MA G.G.10 TOP: 8-2 Example 1 KEY: special right triangles 69. ANS: no; PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: 8-1.2 The Converse of the Pythagorean Theorem NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3 STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.7 | MA G.G.10 TOP: 8-1 Example 4 KEY: Pythagorean Theorem 70. ANS: x = 10, EF = 8, FG = 15 PTS: OBJ: I.2.1 STA: KEY: 71. ANS: 12 1 DIF: L2 1-5.1 Finding Segment Lengths REF: 1-5 Measuring Segments NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP MA G.G.1b | MA G.G.12 segment | segment length TOP: 1-5 Example 2 PTS: 1 DIF: L2 OBJ: 1-5.1 Finding Segment Lengths I.2.1 STA: MA G.G.1b | MA G.G.16 REF: 1-5 Measuring Segments NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP TOP: 1-5 Example 1 KEY: segment | segment length 72. ANS: D PTS: OBJ: I.2.1 STA: KEY: 73. ANS: 61 1 DIF: L3 1-5.1 Finding Segment Lengths PTS: OBJ: STA: KEY: 74. ANS: 113 1 DIF: L3 1-7.2 Constructing Bisectors MA G.G.1b | MA G.G.4 angle bisector REF: 1-5 Measuring Segments NAT: NAEP 2005 M1e | NAEP 2005 M1f | ADP MA G.G.1b | MA G.G.12 TOP: 1-5 Example 3 segment length | segment | midpoint REF: 1-7 Basic Constructions NAT: NAEP 2005 G3b | ADP K.2.2 | ADP K.2.3 TOP: 1-7 Example 4 m PTS: 1 DIF: L2 REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: 8-1.1 The Pythagorean Theorem NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3 STA: MA G.G.1 | MA G.G.1a | MA G.G.2b | MA G.G.7 | MA G.G.10 TOP: 8-1 Example 2 KEY: Pythagorean Theorem | leg | hypotenuse 75. ANS: PTS: 1 DIF: L2 REF: 1-4 Segments, Rays, Parallel Lines and Planes OBJ: 1-4.1 Identifying Segments and Rays NAT: NAEP 2005 G3g STA: MA G.G.1b TOP: 1-4 Example 1 KEY: ray 76. ANS: PTS: OBJ: NAT: STA: KEY: 77. ANS: Z 1 DIF: L3 REF: 7-5 Proportions in Triangles 7-5.1 Using the Side-Splitter Theorem NAEP 2005 G2e | ADP I.1.2 | ADP J.5.1 | ADP K.3 MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 TOP: 7-5 Example 2 corollary of Side-Splitter Theorem PTS: 1 DIF: L3 REF: 1-3 Points, Lines, and Planes OBJ: 1-3.2 Basic Postulates of Geometry NAT: NAEP 2005 G1c | ADP K.1.1 STA: MA G.G.1b TOP: 1-4 Example 4 KEY: point | plane 78. ANS: –19 PTS: OBJ: STA: KEY: 79. ANS: 135 1 DIF: L2 REF: 2-5 Proving Angles Congruent 2-5.1 Theorems About Angles NAT: NAEP 2005 G3g | ADP K.1.1 MA G.G.2b | MA G.G.2c | MA G.G.5 | MA G.G.6 TOP: 2-5 Example 1 vertical angles | Vertical Angles Theorem PTS: OBJ: STA: KEY: 80. ANS: 9 1 DIF: L2 REF: 3-1 Properties of Parallel Lines 3-1.2 Properties of Parallel Lines NAT: NAEP 2005 M1f | ADP K.2.1 MA G.G.2 | MA G.G.2b TOP: 3-1 Example 4 parallel lines | alternate interior angles PTS: OBJ: STA: TOP: 1 DIF: L2 REF: 6-2 Properties of Parallelograms 6-2.2 Properties: Diagonals and Transversals NAT: NAEP 2005 G3f MA G.G.1 | MA G.G.1a | MA G.G.2 | MA G.G.2b | MA G.G.5 | MA G.G.6 6-2 Example 4 KEY: transversal | parallel lines | Theorem 6-4