Reasoning and Proofs Test Geometry Name: _________________________________________ Date: _________________ General Directions: Write your final answers on the space provided. Figures are not drawn to scale. In questions 1-7, write T if true and F if false above the premises and conclusion, then identify the truth value of the whole statement and write it on the space provided on the right. 1. 2. 3. 4. 5. 6. 7. A line has at most two points itself. the intersection of a line and a plane can be the line A plane exists in three noncollinear points and are the same line a point has thickness. the supplement of an acute angle can be acute. Three distinct points will always lie on the same line ray. If two lines are not parallel, then they intersect and and are the same are the same line. The contrapositive of a conditional is logically equivalent to its converse inverse and converse are logically equivalent. If then skew lines doesn’t intersect and aren’t parallel. In questions 8-9, identify the scenario as inductive or deductive reasoning. 8. 9. The scalloped potatoes I took from the oven were cheesy. The enchiladas I took from the oven were cheesy. If I take cookies from the oven, they will be cheesy. Students who study hard get good grades. You are a student who studies hard. You will get good grades. 10. In the sequence, , the next number is 11. Write the correct notation for the shaded region of the Venn Diagram. 12. Is the following argument valid or invalid? 17. 18. 19. 20. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. Question 11 In questions 13-16, use the rules of valid aregument to come to a conclusion. If no conclusion can be reached, write no conclusion. 13. 14. 15. 16. Answers 22. 23. 24. 25. If a persons drives a car, then they have a license. John drives a car. Nick wants to go to the movies on Friday or Saturday night. He did not go on Saturday night. All men are created equal. All people who are created equal are women. My car leaves skid marks if it brakes. I didn’t apply my brakes. In questions 21-24, true or false. 21. Line intersects line . 22. and are coplanar. 23. Line is in plane . 24. and determine a plane. Questions 17-20 25. Which of the following sets of points are contained in exactly one plane? (More than one answer is possible) a. three collinear points d. a line and a point not on the line b. two intersecting lines e. three noncollinear points c. two points f. one point Questions 21-24 Reasoning and Proofs Test Geometry Answers In questions 26-35, identify the statements as 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. or true. Supplementary angles are adjacent to each other. Any two points connected by more than one unique line. Two angles of a linear pair are both obtuse angles. The sum of the measures of two acute angles is greater than the sum of the measures of two obtuse angles. Two lines intersect to form vertical lines. Tw complementary angles are adjacent. Angles that are a linear pair are adjacent. The complement of an obtuse angle is acute. An angle adjacent to a right angle is also a right angle. The supplement of an acute angle is obtuse. In questions 36-39, solve for the indicated measure. 36. If 37. If 38. If 39. If and . is the midpoint of , . is the midpoint of , find the coordinates of and , find and and is in the interior of and and is equidistant from rays and , what is the value of ? . If 48. is complementary to and 49. and 50. If intersect so that and is complementary to . are opposite rays intersected by , then . at . 30. 31. 32. 33. 34. 35. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. Question 45 In questions 47-50, justify each statement using a property, definition, postulate or theorem. 47. If 29. 38. Questions 36-39 45. Find the value of and . 46. Two angles are complementary and one angle has a measure that is nine times the measure of the other angle. What is the measure of the larger angle? 28. 37. 40. is between and . If and , find . 41. If and the supplement of has measure 22°, find . 42. If and are complementary and and are supplementary, then is a(n) __________ angle. 43. is in the interior of . If and , what is ? 44. 27. 36. , find , find . 26. , then and are supplementary. Reasoning and Proofs Test Geometry Complete the proof. 51. Given: is the midpoint of Prove: Statements Reasons 1. ______________________________________ Given 3. ______________________________________ 2. ______________________________________ 4. 5. ______________________________________ 6. 7. ______________________________________ 8. 9. ______________________________________ 10. 52. Given: Definition of congruence Substitution Given ______________________________________ ______________________________________ Simplify Division Property of Equality ______________________________________ is a right angle; Prove: 1. 2. Statements Reasons is a right angle. ______________________________________ 3. and are comp. . 5. and are comp. . 4. 6. 7. ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ ______________________________________ Reasoning and Proofs Test Geometry Write a two-column proof. 53. Given: Prove: ; Statements 54. Given: Prove: bisects Statements Reasons . Reasons