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 Conditional Statements Outline
  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. Biconditional Statements
    • Both the statement and its converse are true
  4. Assignment 2-1: Pg. 71 #2-21, 33, 34
Unit 2-2 Inductive and Deductive Reasoning
  • Standard 2c: Identify, write, and analyze the truth value of conditional statements
  • Standard 2d: Write the inverse, converse, and contrapositive of a conditional statement
Outline
  1. What is Deductive Reasoning?
  2. What is Inductive Reasoning?
    • Finding a Pattern
    • Finding a Counterexample
  3. Assignment 2-2: Pg 80 #3-6, 13, 14...
Unit 2-3 Postulates and Diagrams
  • Standard 2e: Apply the Law of Detachment and the Law of Syllogism in logical reasoning
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 Algebraic Reasoning
  • Standard 2f:Using properties of equality to write algebraic proofs
  • Standard 2g: Identify properties of equality and congruence
Outline
  1. Solving an Equation in Algebra with Justifications
  2. Solving Equations in Geometry with Justifications
    • Properties of Congruence
  3. Assignment 2-4: Pg 96 #3-10
Unit 2-5 Proving Statements about Segments and Angles
  • Standard 2g: Using properties of equality to write algebraic proofs
  • Standard 2h: Identify properties of equality and congruence
Outline
  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 Proving Geometric Relationships
  • Standard 2i: Write Two-Column Proofs
  • Standard 2j: Prove geometric theorems by using deductive reasoning
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