2. 1 Inductive Reasoning & Conjecture 2. 2 Logic 2

Slides:

Advertisements

Similar presentations

Geometry Chapter 2 Terms.

Advertisements

Sec.2-3 Deductive Reasoning

Geometry 2.3 Big Idea: Use Deductive Reasoning

Inductive and Deductive Reasoning Geometry 1.0 – Students demonstrate understanding by identifying and giving examples of inductive and deductive reasoning.

Chapter 2: Geometric Reasoning

Lesson 2-4 Deductive Reasoning. Ohio Content Standards.

Inductive vs Deductive Reasoning

2.3: Deductive Reasoning p Deductive Reasoning Use facts, definitions and accepted properties in logical order to write a logical argument.

Geometry Unit 2 Power Points Montero to 2.3 Notes and Examples Patterns, Conditional Statements, and BiConditional Statements Essential Vocabulary.

Section 2.3 Deductive Reasoning.

Introduction to Geometric Proof Logical Reasoning and Conditional Statements.

Warm Up Underline the hypothesis and circle the conclusion of each conditional. 1. A mapping that is a reflection is a type of transformation. 2. The quotient.

Chapter 2.3 Notes: Apply Deductive Reasoning Goal: You will use deductive reasoning to form a logical argument.

Write the following in biconditional form. p: The sun is out. q: It is day time. The sun is out iff it is day time.

Deductive Reasoning What can you D…D….D…. DEDUCE ?

2.4 DEDUCTIVE REASONING Playing the game of logic well.

Deductive Reasoning Section 2-4. Deductive reasoning uses a rule to make a conclusion. Inductive reasoning uses examples to make a conjecture or rule.

Applying Deductive Reasoning Section 2.3. Essential Question How do you construct a logical argument?

Deductive Reasoning Chapter 2 Lesson 4.

Deductive Reasoning.  Conditional Statements can be written using symbolic notation  p represents hypothesis  q represents conclusion  is read as.

 ESSENTIAL QUESTION  How can you use reasoning to solve problems?  Scholars will  Use the Law of Syllogism  Use the Law of Detachment UNIT 01 – LESSON.

Geometry CH 1-7 Patterns & Inductive Reasoning Using deductive reasoning. Objective.

AGENDA – ALGEBRA 1A SEPT. 3, 2012 (TUESDAY)  Warm-Up  Lesson Logical Reasoning and Counterexamples  Objectives – Identify the hypothesis and conclusion.

Section 2-5: Deductive Reasoning Goal: Be able to use the Law of Detachment and the Law of Syllogism. Inductive Reasoning uses _________ to make conclusions.

WARM UP. DEDUCTIVE REASONING LEARNING OUTCOMES I will be able to use the law of detachment and syllogism to make conjectures from other statements I.

Do Now. Law of Syllogism ◦ We can draw a conclusion when we are given two true conditional statements. ◦ The conclusion of one statement is the hypothesis.

2.2 Inductive and Deductive Reasoning. Deductive reasoning is the process of reasoning logically from given statements to a conclusion.

Ch. 2.3 Apply Deductive Reasoning

Holt Geometry 2-4 Biconditional Statements and Definitions Write and analyze biconditional statements. Objective.

Entry Task. Using Deductive Reasoning 2.4 Learning Target: Given a true statement I can use deductive reasoning to make valid conclusions.

Deductive Reasoning Geometry Chapter 2-3 Mr. Dorn.

Section 2.3: Deductive Reasoning

5-Minute Check Converse: Inverse: Contrapositive: Hypothesis: Conclusion: The measure of an angle is less than 90  The angle is acute If an angle is.

Reasoning and Proof DAY 4: 2.4 Deductive Reasoning.

Inductive Reasoning Notes 2.1 through 2.4. Definitions Conjecture – An unproven statement based on your observations EXAMPLE: The sum of 2 numbers is.

Chapter 2 Section 2.3 Apply Deductive Reasoning. Deductive Reasoning Uses facts, definitions, accepted properties, and the laws of logic to form a logical.

LG 1: Logic A Closer Look at Reasoning

Holt Geometry 2-3 Using Deductive Reasoning to Verify Conjectures Chapter 2.3 – Deductive Reasoning.

Deductive Reasoning BOMLA LacyMath Geometry Pre-AP.

Section 2.3 – Deductive Reasoning

Deductive Reasoning, Postulates, and Proofs

2-3 Apply Deductive Reasoning

Drill: Tuesday, 10/14 2. Determine if the conditional “If x is a number then |x| > 0” is true. If false, give a counterexample. OBJ: SWBAT analyze.

Warm Up For this conditional statement: If a polygon has 3 sides, then it is a triangle. Write the converse, the inverse, the contrapositive, and the.

Objective Apply the Law of Detachment and the Law of Syllogism in logical reasoning.

Apply Deductive Reasoning

Do Now: Name each point , line, and line segment, or ray

Deductive Reasoning Section 2-4.

2-4 Deductive Reasoning Ms. Andrejko.

Applying Deductive Reasoning

Deductive Reasoning Deductive Reasoning – Reasoning that uses facts, rules, definitions, or properties to reach logical conclusions. Law of Detachment.

2.2 Deductive Reasoning Objective:

Sec. 2.3: Apply Deductive Reasoning

2.4 Deductive Reasoning.

2.3 Using Deductive Reasoning to Verify Conjectures

Do Now Determine how a conclusion was made (by observing a pattern, facts being provided, something that is repeated, etc.) 1. Every time Katie has worn.

Warmup Definition: Perpendicular Lines—

2-3 Deductive Reasoning Objectives:

Drill: Tuesday, 10/18 2. Determine if the conditional “If x is a number then |x| > 0” is true. If false, give a counterexample. OBJ: SWBAT analyze.

Math Humor Q: How is a geometry classroom like the United Nations?

2.3 Apply Deductive Reasoning

Drill: Wednesday, 11/1 Determine if the conditional “If x is a number then |x| > 0” is true. If false, give a counterexample. Write the contrapositive.

Notes 2.3 Deductive Reasoning.

Chapter 2.3 Notes: Apply Deductive Reasoning

2-3 Apply Deductive Reasoning

2-4 Deductive Reasoning Deductive Reasoning: Using facts, rules, definitions, or properties to reach logical conclusions. Law of Detachment: A form.

Law of Detachment Law of Syllogism

2-4 Deductive Reasoning Vocab:

Goal 1: Using Symbolic Notation Goal 2: Using the Laws of Logic

Chapter 2.3 Notes: Apply Deductive Reasoning

Presentation transcript:

2. 1 Inductive Reasoning & Conjecture 2. 2 Logic 2 2.1 Inductive Reasoning & Conjecture 2.2 Logic 2.3 Conditional Statements 2-4 Deductive Reasoning Honors Geometry

Main Ideas Use the Law of Detachment Use the Law of Syllogism

Vocabulary Deductive Reasoning uses facts, rules, definitions, or properties to reach logical conclusions. Law of Detachment: If p → q is true and p is true then q is also true. Law of Syllogism: If p → q and q → r is true, then p → r is true.

Law of Detachment If p → q is true and p is true then q is also true If you are a CD teacher, then you have an in-service on September 25th. Given: Mrs. Bayer is a CD teacher. Conclusion:

Law of Detachment If p → q is true and p is true then q is also true If you are a CD teacher, then you have an in-service on September 25th. Given: Mrs. Bayer is a CD teacher. Conclusion: Mrs. Bayer has an in-service on September 25th.

Ex 1: Using Law of Detachment, come up with conclusions for the following: The football team has a game on Friday. Paul is a member of the football team. All cars have 4 wheels A Honda CR-V is a car.

Ex 1: Using Law of Detachment, come up with conclusions for the following: The football team has a game on Friday. Paul is a member of the football team. Paul has a football game on Friday. All cars have 4 wheels A Honda CR-V is a car.

Ex 1: Using Law of Detachment, come up with conclusions for the following: The football team has a game on Friday. Paul is a member of the football team. Paul has a football game on Friday. All cars have 4 wheels A Honda CR-V is a car. A Honda CR-V has 4 wheels.

Law of Syllogism If p → q and q → r is true, then p → r is true. If you wear yoga pants and violate the dress code you will need to go to the office. If you go to the office you will need to change your clothes. If you wear yoga pants and violate the dress code you will need to change your clothes.

Law of Syllogism If p → q and q → r is true, then p → r is true. If you wear yoga pants and violate the dress code, then you will need to go to the office. If you go to the office you will need to change your clothes. If you wear yoga pants and violate the dress code you will need to change your clothes.

Law of Syllogism If p → q and q → r is true, then p → r is true. If you wear yoga pants and violate the dress code, then you will need to go to the office. If you go to the office then you will need to change your clothes. If you wear yoga pants and violate the dress code you will need to change your clothes.

Law of Syllogism If p → q and q → r is true, then p → r is true. If you wear yoga pants and violate the dress code, then you will need to go to the office. If you go to the office then you will need to change your clothes. If you wear yoga pants and violate the dress code then you will need to change your clothes.

Ex last one: Using Law of Syllogism, come up with a valid conclusion for the following: If you attend CDHS then your mascot is the ram. If your mascot is the ram, then your colors are green and white. Perpendicular lines make right angles. All right angles equal 90˚.

Ex last one: Using Law of Syllogism, come up with a valid conclusion for the following: If you attend CDHS then your mascot is the ram. If your mascot is the ram, then your colors are green and white. If you attend CDHS, then your colors are green and white. Perpendicular lines make right angles. All right angles equal 90˚.

Ex last one: Using Law of Syllogism, come up with a valid conclusion for the following: If you attend CDHS then your mascot is the ram. If your mascot is the ram, then your colors are green and white. If you attend CDHS, then your colors are green and white. Perpendicular lines make right angles. All right angles equal 90˚. Perpendicular lines create 90º angles.

Go to textbook page 101