Section 3-6 Inductive Reasoning.

Slides:

Advertisements

Similar presentations

Geometry Chapter 2 Terms.

Advertisements

2.5 If-Then Statements and Deductive Reasoning

Geometry 2.3 Big Idea: Use Deductive Reasoning

Definitions © 2006 by Mr. Mayers Reasoning Conditional Statements Properties Undefined Terms Symmetry Team 1Team 2Team 3Team

Parallel Lines and Planes Section Definitions.

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

Chapter 2: Geometric Reasoning

Angles of a Polygon and Inductive Reasoning 3.5 AND 3.6.

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.

Section 1.1 Inductive Reasoning 1/16. DEDUCTIVE REASONING Two Types of Reasoning INDUCTIVE REASONING 2/16.

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

How to do a Proof Using Uno!. What does it mean to prove something? PROOF (pruf) –noun 1. evidence sufficient to establish a thing as true, or to produce.

Chapter 2.1 Common Core G.CO.9, G.CO.10 & G.CO.11 Prove theorems about lines, angles, triangles and parallelograms. Objective – To use inductive reasoning.

Laws of Logic. Deductive Reasoning Uses the following to form logical arguments. Facts Example: All humans breath air. Definitions Example: Two lines.

Section 2.3 Deductive Reasoning.

Introduction to Geometric Proof Logical Reasoning and Conditional Statements.

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

Section 2-3 Deductive Reasoning. Types of Reasoning:

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

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

Deductive Reasoning Chapter 2 Lesson 4.

Honors Geometry Intro. to Deductive Reasoning. Reasoning based on observing patterns, as we did in the first section of Unit I, is called inductive reasoning.

2.4 Ms. Verdino.  Biconditional Statement: use this symbol ↔  Example ◦ Biconditional Statement: The weather is good if and only if the sun is out 

Postulates and Paragraph Proofs Section 2-5.  postulate or axiom – a statement that describes a fundamental relationship between the basic terms of geometry.

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.

Entry Task Write down your age Multiply it by 10 Add 8 to the product Double that answer and subtract 16 Divide the result by 20 Explain what you notice.

Ch. 2.3 Apply Deductive Reasoning

2.3 Deductive Reasoning Geometry. Standards/Objectives Standard 3: Students will learn and apply geometric concepts. Objectives: Use symbolic notation.

Lesson 21 LAW OF DETACHMENT AND SYLLOGISM. Review and New Vocabulary Inductive reasoning is the process of reasoning that a rule or statement is true.

Section 2-4: Deductive Reasoning Objectives: Use the Law of Detachment Use the Law of Syllogism Inductive Reasoning: based on observing what has happened.

Section 2.3: Deductive Reasoning

Bell Work If 2 Lines are skew, then they do not intersect 1) Converse 2) Inverse 3) Contrapositive 4) Biconditional.

2.3 Deductive Reasoning. Symbolic Notation Conditional Statements can be written using symbolic notation. Conditional Statements can be written using.

2.5 Postulates and Proofs GEOMETRY. Postulate (axiom)- a statement that is accepted as true without proof 2.1: Through any two points, there is exactly.

Section 3.6 Reasoning and Patterns. Deductive Reasoning Deductive reasoning starts with a general rule, which we know to be true. Then from that rule,

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

Reasoning and Proof Chapter Use Inductive Reasoning Conjecture- an unproven statement based on an observation Inductive reasoning- finding a pattern.

Chapter 2, Section 1 Conditional Statements. Conditional Statement Also know as an “If-then” statement. If it’s Monday, then I will go to school. Hypothesis:

Deductive Reasoning. Warm-up Objectives: 1) To use the Law of Detachment 2) To use the Law of Syllogism.

LG 1: Logic A Closer Look at Reasoning

PROOFS. Geometry "measuring the earth“ is the branch of math that has to do with spatial relationships.

USING PROPERTIES FROM ALGEBRA ALGEBRAIC PROPERTIES OF EQUALITY Let a, b, and c be real numbers. SUBTRACTION PROPERTY ADDITION PROPERTY If a = b, then a.

Deductive Reasoning BOMLA LacyMath Geometry Pre-AP.

2-4 Deductive Reasoning Objective:

Reasoning and Proof Unit 2.

Section 2.3 – Deductive Reasoning

Deductive Reasoning, Postulates, and Proofs

2-3 Apply Deductive Reasoning

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.

2.2 Inductive and Deductive Reasoning

Section 2-3: Deductive Reasoning

Applying Deductive Reasoning

Sec. 2.3: Apply Deductive Reasoning

Earlier we learned about inductive reasoning. • Earlier we learned about inductive reasoning. • Look at specific examples. • Recognize patterns, which.

Parallel Lines and Planes

2.4 Deductive Reasoning.

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.

2.3 Apply Deductive Reasoning

Premise: If it’s a school day, then I have Geometry class.

Chapter 2.3 Notes: Apply Deductive Reasoning

Reasoning and Proofs Deductive Reasoning Conditional Statement

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.

Chapter 2: Geometric Reasoning

Law of Detachment Law of Syllogism

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

Chapter 2.3 Notes: Apply Deductive Reasoning

Chapter 2 Reasoning and Proof.

Presentation transcript:

Section 3-6 Inductive Reasoning

Types of Reasoning:

Inductive Reasoning Conclusion based on several past observations The conclusion is probably true, but not necessarily true Uses words like noticed and observed

Example: For 3 weeks, the cafeteria served pizza on Wednesday. I conclude that next Wednesday the cafeteria will have pizza.

Deductive Reasoning Conclusion based on accepted statements: Definitions, postulates, previous theorems, corollaries and given information

Conclusion must be true if the hypotheses are true. Logical Argument (follows logical order)

Example: Dictionaries are useful books. Useful books are valuable. Therefore, dictionaries are valuable.

Two laws of Deductive Reasoning:

Law of Detachment If p  q is a true conditional statement and p is true, then q is true. 2 pieces of information: p and q

Example: If I pass the test, then I get an A in geometry. I passed the test. I get an A in Geometry.

Law of syllogism If p  q and q  r are true conditional statements, then p  r is true. Similar to the Transitive property in algebra 3 pieces of information: p, q and r

Example: If people live in Manhattan, then they live in New York. If people live in New York, then they live in the United States. If people live in Manhattan, then they live in the United States.