Geometry
Chapter 2 Geometric Reasoning
Unit 2-1 Using Inductive Reasoning to Make Conjectures
- Standard 2a: Use inductive reasoning to identify patterns and make conjectures.
- Standard 2b: Find counterexamples to disprove conjectures.
Agenda
- What is Deductive Reasoning?
- What is Inductive Reasoning?
- Finding a Pattern
- Finding a Counterexample
- Assignment 2-1: Pg. 77 #2, 3, 5, 6, 12, 17, 19
Unit 2-2 Conditional Statements
- Standard 2c: Identify, write, and analyze the truth value of conditional statements
- Standard 2d: Write the inverse, converse, and contrapositive of a conditional statement
Agenda
- 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?
- 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
- Assignment 2-2: Pg 84 #1-10, 13, 14, 16-18, 34-36
Unit 2-3 Using Deductive Reasoning to Verify Conjectures
- Standard 2e: Apply the Law of Detachment and the Law of Syllogism in logical reasoning
Agenda
- Law of Detachment in Conditional Statements: Prove the hypothesis and you've proven the conclusion
- Law of Syllogism: The Law of Detachment and the Transitive Property in Logic
- Conditional Statement Activity
- Write a conditional statement (clearly identify hyptothesis & conclusion)
- Write its conditional, inverse, and contrapositive
- State the truth value of each of your four statements
- Assignment 2-3: Pg. 91 #2-7
Unit 2-4 Biconditional Statements & Definitions
- Standard 2f: Write and Analyze Biconditional Statements
Agenda
- 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?
- Assignment 2-4: Pg 102 #10, 11, 15, 17, 18
Unit 2-5 Algebraic Proof
- Standard 2g: Using properties of equality to write algebraic proofs
- Standard 2h: Identify properties of equality and congruence
Agenda
- Solving an Equation in Algebra with Justifications
- Solving Equations in Geometry with Justifications
- Assignment 2-5: Part A Pg 107 #1-15 Part B Pg 108 #16-21, 23, 24, 33
Unit 2-6 Geometric Proofs
- Standard 2i: Write Two-Column Proofs
- Standard 2j: Prove geometric theorems by using deductive reasoning
Agenda
- Using Deductive Reasoning to Write a Geometric Proof
- Definitions
- Postulates
- Preperties
- Theorems
- Completing a Two Column Proof
- Writing a Two Column Proof
- 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
- Standard 2k: Write Flowchart and Paragraph Proofs
- Standard 2l: Prove geometric theorems by using deductive reasoning
Agenda
- Assignment 2-7: