Geometry CP 2.1-2.5 Review WS Name 1. a) Use inductive reasoning to sketch the fourth figure in each pattern. Figure 4 b) How many squares are in the next object? 2. Use inductive reasoning to write the next three numbers in each pattern and describe the pattern. a) 1, 4, 16, 64,. b) 6, 1, 4, 9,... Find a counterexample to disprove the following two conjectures. 3. Conjecture The quotient of two numbers is always smaller than the dividend. 4. Conjecture Every triangle is three congruent sides. Rewrite the conditional statements in if-then form. 5. You have a fever if your body temperature is 103 F. _ 6. A deer with white fur and pink eyes is albino. _ 7. An obtuse angle is an angle that measures more than 90 degrees and less than 180 degrees. _
For the given conditional, underline the hypothesis once and the conclusion twice. Then write the converse, the inverse, and the contrapositive and indicate whether each statement is true or false. 8. If it rains then it pours. T or F Converse: T or F Inverse: T or F Contrapositive: T or F 9. If an angle measures 34, then it is an acute angle. T or F Converse: T or F Inverse: T or F Contrapositive: T or F 10. The and the are equivalent statements. 11. The and the are equivalent statements. What does it mean to be equivalent statements? Rewrite the following conditional as a biconditional statement. 12. If a point is the midpoint of a segment then it divides the segment into two congruent segments. 13. Two angles are complementary angles if the sum of their measures is 90. 14. Explain the difference between inductive and deductive reasoning.
15. Exploration of the surface of Mars has produced some surprising facts. Therefore exploration of the surface of Jupiter will produce some surprising facts. 16. If it is above 80 degrees outside, then I always turn the air conditioning on. Today it is going to be 98 degrees. You conclude that I will turn my air conditioning on. 17. All dogs are mammals. All mammals have kidneys. Therefore all dogs have kidneys. 18. All swans we have seen have been white; therefore all swans are white. Use the Law of Detachment to make a valid conclusion in the true situation. 19. If two angles have the same measure, then they are congruent. You know that m A = m B. 20. Jesse goes to the gym every weekday. Today is Monday. If possible, use the Law of Syllogism to write the conditional statement that follows from the pair of true statements. 21. If Ron eats lunch today, then he will eat a sandwich. If Ron eats a sandwich, then he will drink a glass of milk.
22. If x 2 > 36, then x 2 > 30. If x > 6, then x 2 > 36. 23. If a triangle is equilateral, then all of its sides are congruent. If a triangle is equilateral, then all angles in the interior of the triangle are congruent. State the law of logic that is illustrated below. 24. If you do your homework, then you can watch TV. If you watch TV, then you can watch your favorite show. If you do your homework, then you can watch your favorite show. Can the statement be assumed to be true from the diagram for #25-29? Explain your answer. 25. EF plane S 26. EF CG 27. D, C, and H are collinear. 28. E, C, and F are collinear. 29. EF intersects plane S at point C In Exercises 30-34, use the diagram to determine if the statement is true or false. 30. Points A, B, D, and J are coplanar. 31. EBA is a right angle. 32. Points E, G lie on plane H 33. ABD and EBC are vertical angles. 34. GCA and CBD are congruent angles. Complete the logical argument by giving a reason for each step. 35. 8x 34 = 6 Given a. 8x = 40 a. b. x = 5 b.
36. 4x 7 = 6x + 7 Given a. 2x 7 = 7 a. b. 2x = 14 b. c. x = 7 c. 37. 5(x 3) = 4(x + 2) Given a. 5x 15 = 4x + 8 a. b. x 15 = 8 b. c. x = 23 c. Use the property to complete the statement. 38. Addition Property of Equality: if RS = TU, then RS + 20 =. 39. Multiplication Property of Equality: If m 1 = m 2, then 3m 1 =. 40. Substitution Property of Equality: If a = 20, then 5a =. 41. Reflexive Property of Equality: If x is a real number, then x =. 42. Symmetric Property of Equality: If AB = CD, then CD =. 43. Transitive Property of Equality: If m E = m F and m F = m G, then. In exercises 44-46, name the property. 44. If RST XYZ, then XYZ RST. 45. PQ PQ 46. If FG JK and JK LM, then FG LM. Use the diagram to the right to name the property for #47-49. 47. AB BC AC 48. ABD DBC ABC D 49. If AB BC then AB 10 BC 10 A B C