Chapter 1 Lessons 1-4 to 1-8

1-4 Inductive Reasoning Conjecture – an unproven statement or rule that is based on inductive reasoning. Counter Example – an example that shows/proves a statement or conjecture is false. Inductive Reasoning – a type of reasoning that reaches conclusions based on a pattern of specific examples.

Examples: Leave Room For Examples! Between Every Lesson!

1-5 Conditional Statements Conditional – is an “if-then” statement that relates a hypothesis and Conclusion. Hypothesis – is the part of a conditional Statement that follows “If” Conclusion – Is the part of a conditional statement that follows “Then” Truth Value – is “t” or “f” based on whether the statement is “True” or “False.” Converse – reverses the hypothesis and the conclusion. Negation – “Not” or opposite of original statement. Inverse – Is negating hypothesis and conclusion in conditional statement. Contrapositive – negating hypothesis and conclusion of converse or negating and reversing conditional statement. Biconditional – combining conditional and converse statement is “if and only if”

Examples: Leave Room For Examples! Between Every Lesson!

1-6 Deductive Reasoning Deductive Reasoning – the process of reasoning using given and previously known facts to reach a logical conclusion. Law of Detachment – Law of logic that states if a conditional statement and its hypothesis are true, then its conclusion is also true. Law of Syllogism – 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.

Examples: Leave Room For Examples! Between Every Lesson!

1-7 Writing Proofs 1-8 indirect Proofs Proof – a convincing argument that uses deductive reasoning. Theorem – A conjecture that is proven Two – column Proof – argument in which statements and reasons are aligned into two columns. Paragraph Proof – Argument in which Statements and reasons are connected in sentences. 1-8 indirect Proofs Indirect proof – a proof using indirect reasoning.

Theorem 1-1 Vertical Angles Theorem – Vertical Angles are congruent. Theorem 1-2 Congruent Supplements Theorem – If two angles are supplementary to congruent angles (or the same angle) then they are congruent. Theorem 1-3 Congruent Compliments Theorem – If two angles are complementary to congruent angles (or the same angle), then they are congruent.