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.