Geometry

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Across
  1. 3. A counterexample is an example that shows a statement or conjecture is false.
  2. 5. reasoning: Inductive reasoning is a type of reasoning that reaches conclusions based on a pattern of specific examples or past events.
  3. 6. of syllogism: The Law of Syllogism is a law of logic that states that given two true conditionals with the conclusion of the first being the hypothesis of the second, there exists a third true conditional having the hypothesis of the first and the conclusion of the second. Symbolically, if p → q and q → r are true, then p → r is true.
  4. 8. The opposite meaning of a statement.
  5. 9. combination of a conditional statement ,p-> q , and its converse q->p. A biconditional contains the words “if and only if “
  6. 10. reasoning: Deductive reasoning is a process of reasoning using given and previously known facts to reach a logical conclusion
  7. 11. of detachment: The Law of Detachment is a law of logic that states if a conditional statement and its hypothesis are true, then its conclusion is also true. Symbolically, if p → an and p are true, then q is true.
  8. 13. A proof is a convincing argument that uses deductive reasoning. A proof can be written in many forms. In a two-column proof, the statements and reasons are aligned in columns. In a paragraph proof, the statements and reasons are connected in sentences. In a flow proof, arrows show the logical connections between the statements. In a coordinate proof, a figure is drawn on a coordinate plane and the formulas for slope, midpoint, and distance are used to prove properties of the figure. An indirect proof involves the use of indirect reasoning.
  9. 14. The inverse is obtained by negating both the hypothesis and the conclusion of a conditional. The inverse of the conditional "if p, then q" is the conditional "if not p, then not q."
Down
  1. 1. geometric figure made with only a straightedge and compass
  2. 2. converse reverses the hypothesis and conclusion of a conditional.
  3. 3. The contrapositive is created by negating and reversing a conditional statement. For "if p, then q," the contrapositive is "if not q, then not p." They have the same truth value.
  4. 4. if-then statement that relates a hypothesis, the part that follows if, to a conclusion, the part the follows then.
  5. 7. bisector: A ray that divides an angel into two congruent angels.
  6. 12. An unproven statement or rule that is based on inductive reasoning