Geometry

Chapter 2    Geometric Reasoning
Unit 2-1 Unit 2-2 Unit 2-3 Unit 2-4 Unit 2-5 Unit 2-6 Unit 2-7
Unit 2-1 Using Inductive Reasoning to Make Conjectures Agenda
  1. What is Deductive Reasoning?
  2. What is Inductive Reasoning?
    • Finding a Pattern
    • Finding a Counterexample
  3. Assignment 2-1: Pg. 77 #2, 3, 5, 6, 12, 17, 19
Unit 2-2 Conditional Statements Agenda
  1. What is a Conditional Statement?
    • The Hypothesis is the "if" statement
    • The Conclusion is the "then" statement
    • If p is true then q is true or p → q
    • How do we determine if the statement is true or false?
  2. Related Conditional Statements
    • Converse: If q is true then p is true or q → p
    • Inverse: If p is not true then q is not true or ~p →~q
    • Contrapositive: If q is not true then p is not true or ~q → ~p
  3. Assignment 2-2: Pg 84 #1-10, 13, 14, 16-18, 34-36
Unit 2-3 Using Deductive Reasoning to Verify Conjectures Agenda
  1. Law of Detachment in Conditional Statements: Prove the hypothesis and you've proven the conclusion
  2. Law of Syllogism: The Law of Detachment and the Transitive Property in Logic
  3. Conditional Statement Activity
    1. Write a conditional statement (clearly identify hyptothesis & conclusion)
    2. Write its conditional, inverse, and contrapositive
    3. State the truth value of each of your four statements
  4. Assignment 2-3: Pg. 91 #2-7
Unit 2-4 Biconditional Statements & Definitions Agenda
  1. What is a Biconditional Statement
    • Both the statement and its converse are true
    • "Iff" which is shorthand for "if and only if"
    • Are any of your conditional statements from the activity in 2-3 biconditional?
  2. Assignment 2-4: Pg 102 #10, 11, 15, 17, 18
Unit 2-5 Algebraic Proof Agenda
  1. Solving an Equation in Algebra with Justifications
  2. Solving Equations in Geometry with Justifications
    • Properties of Congruence
  3. Assignment 2-5: Part A Pg 107 #1-15 Part B Pg 108 #16-21, 23, 24, 33
Unit 2-6 Geometric Proofs Agenda
  1. Using Deductive Reasoning to Write a Geometric Proof
    • Definitions
    • Postulates
    • Preperties
    • Theorems
  2. Completing a Two Column Proof
  3. Writing a Two Column Proof
  4. Assignment 2-6: Part A Guided Practice #1-4 Part B #6-8, 11-13, 16-22, 26
Unit 2-7 Flowchart and Paragraph Proofs Agenda
  2. Assignment 2-7: