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Geometry Unit 2: Reasoning and Proof Name: _______________________________________________________ Date: _______________________ Given x, y, and z are real numbers. Use the given property or properties of equality to fill in the blank in each of the following questions. 1. 2. 3. 4. 5. 6. 7. Symmetric: If x = 3, then _______________________________________. Reflexive: If x + 2 = 9, then _____________________________________. Transitive: If y = 12 and x = y, then __________________________________________. Symmetric: If x + y = y + z, then ____________________________________________. Reflexive: If x + y = y + z, then _____________________________________________. Substitution: If x = y – 7 and x = z + 4, then _____________________________________________. Use the transitive property of equality to write a convincing logical argument (a proof) that the statement below is true. If a = b and b = c and c=d and d=e, then a=e. Geometry Unit 2: Reasoning and Proof Name: _______________________________________________________ Date: _______________________ Given x, y, and z are real numbers. Use the given property or properties of equality to fill in the blank in each of the following questions. 1. 2. 3. 4. 5. 6. 7. Symmetric: If x = 3, then _______________________________________. Reflexive: If x + 2 = 9, then _____________________________________. Transitive: If y = 12 and x = y, then __________________________________________. Symmetric: If x + y = y + z, then ____________________________________________. Reflexive: If x + y = y + z, then _____________________________________________. Substitution: If x = y – 7 and x = z + 4, then _____________________________________________. Use the transitive property of equality to write a convincing logical argument (a proof) that the statement below is true. If a = b and b = c and c=d and d=e, then a=e. Let M be the relation “is the mother of.” Let B be the relation “if the brother of.” 8. Is M symmetric? Explain your answer. 9. Is B symmetric? Explain your answer. 10. Is M transitive? Explain your answer. 11. Is B transitive? Explain your answer. 12. Let w, x, y, and z be real numbers. Prove: If w = y and x = z, then w + x = y + z. 13. The following statement is NOT true. “Let A, B, C, D, E, and F be points. If AB = DE and BC = EF, then AC = DF. Draw a diagram with these points shown to provide a counterexample. Let M be the relation “is the mother of.” Let B be the relation “if the brother of.” 8. Is M symmetric? Explain your answer. 9. Is B symmetric? Explain your answer. 10. Is M transitive? Explain your answer. 11. Is B transitive? Explain your answer. 12. Let w, x, y, and z be real numbers. Prove: If w = y and x = z, then w + x = y + z. 13. The following statement is NOT true. “Let A, B, C, D, E, and F be points. If AB = DE and BC = EF, then AC = DF. Draw a diagram with these points shown to provide a counterexample.