| | | |Chapter 1 – Tools of Geometry |Chapter 2 – Logic and Reasoning | | | | |[pic] |Conditional: an if-then statement | |[pic] |Hypothesis: the if part of a conditional (p) | |Segment Addition Postulate: AC + CB = AB |Conclusion: the then part of a conditional (q) | | | | |[pic] |Conditional: [pic] | |Adjacent angles: 3 and 4 |Converse: [pic] (swap hypothesis and conclusion) | |Vertical angles: 2 and 3 ([pic]) |Inverse:[pic](negate hypothesis and conclusion) | |Linear pair: 1 and 3 (sum = 180 |Contrapositive:[pic](negate and swap both) | | | | |Collinear: on the same line |A conditional and its contrapositive are logical equivalents. | |Coplanar: in the same plane | | |Skew lines: Non-coplanar lines and never intersect |Biconditional: a conditional and its converse are both true and combined | | |into one statement with “if and only if” | |Distance formula:[pic] | | |Midpoint formula:[pic] |Definitions are biconditionals | |Undefined terms: point, line, and plane | | |Postulate (or Axiom): accepted as true, not proven |Counterexample: a specific example where the hypothesis of a conditional is | |Theorem: something that is proven |true but the conclusion is false. | | | | | |Law of detachment: | | |If it is raining, then I wear a raincoat. It is raining. | | |Conclusion: I wear a raincoat | | | | |...

| | | |Chapter 1 – Tools of Geometry |Chapter 2 – Logic and Reasoning | | | | |[pic] |Conditional: an if-then statement | |[pic] |Hypothesis: the if part of a conditional (p) | |Segment Addition Postulate: AC + CB = AB |Conclusion: the then part of a conditional (q) | | | | |[pic] |Conditional: [pic] | |Adjacent angles: 3 and 4 |Converse: [pic] (swap hypothesis and conclusion) | |Vertical angles: 2 and 3 ([pic]) |Inverse:[pic](negate hypothesis and conclusion) | |Linear pair: 1 and 3 (sum = 180 |Contrapositive:[pic](negate and swap both) | | | | |Collinear: on the same line |A conditional and its contrapositive are logical equivalents. | |Coplanar: in the same plane | | |Skew lines: Non-coplanar lines and never intersect |Biconditional: a conditional and its converse are both true and combined | | |into one statement with “if and only if” | |Distance formula:[pic] | | |Midpoint formula:[pic] |Definitions are biconditionals | |Undefined terms: point, line, and plane | | |Postulate (or Axiom): accepted as true, not proven |Counterexample: a specific example where the hypothesis of a conditional is | |Theorem: something that is proven |true but the conclusion is false. | | | | | |Law of detachment: | | |If it is raining, then I wear a raincoat. It is raining. | | |Conclusion: I wear a raincoat | | | | |...