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IM 2 MIDTERM REVIEW (To receive credit you must show work and not just give an answer) CHAPTER 1 1. What is the distance between the two points (-5, 2) and (-6, 10) a. 13.6 c. 8.1 b. 12.0 d. 16.3 2. What is the midpoint of a line segment with endpoints (-5, 2) and (-6, 10)? a. (-5.5, 6) b. (0.5, -4) c. (-1.5, 2) d. (5.5, 6) 3. <ABC is bisected with D on the bisector. If the measure of <ABC is 112 degrees, what is the measure of <CBD? a. 112 b. 56 c. 224 d. 66 CHAPTER 2 4. Which of the following is NOT an example of deductive reasoning? a. Tabitha reads that the sum of the measures of the interior angles of a triangle is , of a quadrilateral is , and of a pentagon is . She concludes that the sum of the measures of the interior angles of an n-gon is . b. At her part-time job, Emma earns $8.75 per hour. Emma determines that she will earn $175 for working 20 hours. c. James learns in health class that 60 minutes of exercise per day greatly reduces a person’s levels of LDL cholesterol. He begins exercising 60 minutes per day, and concludes that he is reducing his levels of LDL cholesterol. d. In trigonometry class, Raul learns that the mnemonic SOHCAHTOA can help him remember the definitions of the trigonometric ratios sine, cosine, and tangent. On a test, Raul is asked to define the term sine. He uses the mnemonic to answer that . 5. The first four numbers in a sequence are 1, 4, 9, and 16. Patrice determines the next number is 25. What type of reasoning did he use to determine this number? a. Inductive b. Deductive c. d. Neither inductive or deductive Both inductive and deductive 6. In the triangle shown, ` and . What could you use to prove that a. Definition of a midpoint b. Definition of congruent segments c. Segment addition postulate d. Addition property of equality ? 7. Which of the following is TRUE about a Theorem? a. it does not have to be proven b. it must be proven c. it is the same as a postulate d. it is taken as truth 8. Read the proof of the same side exterior angles converse theorem. What are the two missing reasons from the proof? a. b. c. d. definition of supplementary angles; corresponding angles theorem definition of supplementary angles; corresponding angles converse theorem Substitution; corresponding angles converse theorem Substitution; corresponding angles theorem CHAPTER 3 9. Find the measure of angle 4. Then classify the triangle. a. 145; obtuse b. 35; right c. 145; acute d. 35; acute 10. Find the measure of angle 4. a. 40 b. 130 c. 65 d. 100 11. The figure shows intersecting lines. Which choice shows vertical angles? a. <RVW and <TVX b. <YVT and <SVZ c. <TVS and <WVU d. <TVS and <UVR 12. The parks and recreation organization has decided to add a sidewalk around a big oak tree in the park. Its members are hoping that this will decrease the amount of foot traffic in front of the tree. The diagram shows the old and new sidewalks. About how many additional feet will people travel if they walk along the new path? a. 18 feet c. 45feet b. 24 feet d. 51 feet 13. Find the value of a and b. a. a = 8√3 ; b = 8 kilometers b. a = 16 kilometers; b = 8√3 c. a = 8 kilometers; b = 16 kilometers d. a = 8 kilometers; b = 8√3 14. Triangle ABC is an equilateral triangle. What is the area of the triangle? a. √2 square units b. √3 Square units c. 23 Square units d. 2 Square units 15. What is the area of the square? a. 52 Square units c. 50 Square units b. 252 Square units d. 100 Square units 16. The lengths of two sides of a triangle are 3 inches and 7 inches. Which of the following lengths could be the length of the third side? a. 4 c. 10 b. 3 d. 9 CHAPTER 4 17. An oil company needs to place a pipeline to the bottom of the ocean 70 meters from the shore. They measure the depth at 10 meters from shore to be 2 meters. They know that the ocean depth increases at a gradual rate. How deep is the part of the ocean where they will place the pipeline? a. 12 meters deep b. 14 meters deep b. 62 meters deep d. 15 meters deep 18. Solve for x. a. 21.9 b. 8.9 b. 9.8 d. 240 19. Victoria holds a 5 foot long fishing pole. The fishing line extends 3 feet to the water’s surface and then another 12.6 feet to a hook. How far is the fish from the hook? a. b. c. d. 21 ft 24.6 ft 27 ft 30.6 ft 20. In triangle ABC, what is the value of x? a. b. c. d. 11 14 15.6 16.2 21. Solve for x in the figure shown. a. b. c. d. CHAPTER 5-6 22. Write the inverse of the following statement: If a quadrilateral is a rhombus, then the quadrilateral is a parallelogram. a. b. c. d. If a quadrilateral is a parallelogram, then the quadrilateral is a rhombus If a quadrilateral is not a rhombus, then the quadrilateral is not a parallelogram If a quadrilateral is not a rhombus, then the quadrilateral is a parallelogram If a quadrilateral is not a parallelogram, then the quadrilateral is not a rhombus 23. Determine what information is sufficient to prove that triangle ABC is congruent to triangle XYZ. a. b. c. d. 24. Which set of congruence statements shows that Theorem? by the SAS Congruence a. c. b. d. 25. The image in this figure was formed by rotating statement that describes these triangles? a. b. c. d. about the origin. What is a congruence 26. Which set of congruence statements show that by the SSS Congruence Theorem? a. c. b. d. 27. Using the diagram shown, choose the correct conclusion. a. b. c. d. The triangles are congruent by HL. The triangles are congruent by ASA. The triangles are congruent by AAS. Not enough information to determine if the triangles are congruent. Chapter 12 28. Which is the absolute maximum of the function 𝒇(𝒙) = −𝒙𝟐 + 𝟔𝒙 a. b. c. d. (3, 9) (0, 0) (3, 0) (4, 2) 29. What are the x-intercepts of the function a. ) and b. (1, 0) and (5, 0) c. d. (4, 0) and (12, 0) 30. The axis of symmetry of a parabola is the parabola? , and one point on the parabola is (3, 8). What is another point on a. (2, 2) b. (2, 14) c. d. (9, 8) 31. Which of these functions has a y-intercept of (0, 1)? a. b. c. d. 32. What is the vertex of a parabola represented by the function the parabola are and if two symmetric points on a. (-2,-9) b. (2, 12) c. d. 33. Two symmetric points on a parabola are (2,-1) and (6,-1). What is the parabola’s axis of symmetry? a. b. c. d. 34. Which is the equation of a parabola that opens upward and has a vertex at the point (2,-6)? a. b. c. d. 35. What is the range of the function represented by the graph? a. b. c. d. All real numbers greater than 4. All real numbers less than . All real numbers greater than . All real numbers less than . 36. Which function represents a parabola that has zeroes at (3, 0) & (-4, 0)? a. b. c. d. 37. What is the interval of increase for the function represented by the graph? a. b. c. d. ANSWER KEY: 1. C 2. A 3. B 4. A 5. A 6. C 7. B 8. C 9. C 10. D 11. D 12. A 13. D 14. B 15. C 16. D 17. B 18. A 19. A 20. D 21. C 22. B 23. C 24. D 25. D 26. C 27. C 28. A 29. A 30. D 31. B 32. C 33. C 34. B 35. C 36. A 37. D