1. Chapter 1
Lessons 1-4 to 1-8

2. 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.

3. Examples:
Leave Room For Examples! Between Every Lesson!

4. 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”

5. Examples:
Leave Room For Examples! Between Every Lesson!

6. 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.

7. Examples:
Leave Room For Examples! Between Every Lesson!

8. 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.

9. 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.