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

Slides:

Advertisements

Similar presentations

Types of Triangles Scalene A triangle with no congruent sides

Advertisements

Geometry Chapter 2 Terms.

Introduction to Geometry – Postulates and Theorems

2.5 If-Then Statements and Deductive Reasoning

Geometry 2.3 Big Idea: Use Deductive Reasoning

Chapter 2 Geometric Reasoning

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

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

Introduction to Geometric Proof Logical Reasoning and Conditional Statements.

1 2-3 Deductive Reasoning Objectives: Define deductive reasoning Use the Law of Detachment Use the Law of Syllogism.

» Please sit by your number from the seating chart on the clipboard. » Please fill in the vocabulary sheet on your desk: ˃Conditional statement ˃Hypothesis.

Monday Wake Up 1. Tell me one thing you did over the weekend. 2.What is the difference between a paragraph proof and a column proof? 3.True or False: If.

Today’s Lesson is on DEDUCTIVE REASONING.

Section 2-3 Deductive Reasoning. Types of Reasoning:

Bell Work “If x=4, then “ 1)Write the hypothesis 2)Write the Conclusion 3) Write the converse 4)What is the Biconditional?

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

2.4 Deductive Reasoning Deductive Reasoning – Sometimes called logical reasoning. – The process of reasoning logically from given statements or facts to.

1.1 Introduction to Inductive and Deductive Reasoning

Deductive Reasoning Chapter 2 Lesson 4.

Chapter 2 Lesson 3 Objective: To use the Law of Detachment and the Law of Syllogism.

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 

2.2 Inductive and Deductive Reasoning. What We Will Learn Use inductive reasoning Use deductive reasoning.

Deductive Structure Statements of Logic. The Structure.

2.4 Deductive Reasoning. Essential Vocabulary Deductive reasoning - is the process of reasoning logically from given statements to a conclusion Law.

Deductive Structure Lesson 1.7. Deductive Structure: Conclusions are justified by means of previously assumed or provided statements.

Warm-up - Sept 22 (Tuesday) 8. Which conditional and its converse form a true biconditional? a. Write the two conditional statements that make up this.

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

Chapter 2 Section 2.1 – Conditional Statements Objectives: To recognize conditional statements To write converses of conditional statements.

Section 2.3: Deductive Reasoning

Properties, Postulates, & Theorems Conditionals, Biconditionals,

1.What is the difference between a paragraph proof and a column proof? 2.True or False: If a quadrilateral is a square, then all four sides are congruent.

If – Then Statements How can you use if-then statements in deductive reasoning? How is deductive reasoning different from inductive reasoning?

Reasoning and Proof DAY 4: 2.4 Deductive Reasoning.

Draw a Logical Conclusion:  If you are a lefty then you struggle to use a can opener.  If you like math then you must be smart.  If you are smart then.

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:

Conditional Statements and Deductive Reasoning 2-1 – 2-3.

2.3 Deductive Reasoning 2.4a Reasoning in Algebra.

Conditional Statements. 1) To recognize conditional statements and their parts. 2) To write converses, inverses, and contrapositives of conditionals.

Geometry Chapter 2: Reasoning and Introduction to Proof We can do this dude!

LG 1: Logic A Closer Look at Reasoning

2-4 Deductive Reasoning.

Chapter 2: Reasoning & Proof Conditionals, Biconditionals, & Deductive Reasoning.

2-4 Deductive Reasoning. Deductive Reasoning …(sometimes called Logical Reasoning) is the process of reasoning logically from given statements or facts.

If your cable company keeps you on hold, then you get _________. If you get _________, then you go _______________. If you go _______________, then accidents.

2-4 Deductive Reasoning Objective:

Reasoning and Proof Unit 2.

Deductive Reasoning, Postulates, and Proofs

Biconditionals & Deductive Reasoning

POSTULATES AND PROOFS ★Postulates are statements that are assumed to be true without proof. ★ Postulates serve two purposes - to explain undefined terms,

Reasoning and Proofs Chapter 2.

2.2 Inductive and Deductive Reasoning

Entry Task Complete the Solve It activity on the top of page 106.

Do Now: True 2. False 3. False C D.

2.1: Patterns and Inductive Reasoning

Section 2-3: 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.

2.4 Deductive Reasoning.

Warmup Write the two conditionals(conditional and converse) that make up this biconditional: An angle is acute if and only if its measure is between 0.

Introduction to Geometry – Postulates and Theorems

2-3 Deductive Reasoning Objectives:

Vocabulary inductive reasoning conjecture counterexample

2.3 Apply Deductive Reasoning

Deductive Reasoning BIG IDEA: REASONING AND PROOF

Section 3-6 Inductive Reasoning.

2.3 Deductive Reasoning.

1.1 Introduction to Inductive and Deductive Reasoning

Lesson 2-R Chapter 2 Review.

Presentation transcript:

Deductive Reasoning

Warm-up

Objectives: 1) To use the Law of Detachment 2) To use the Law of Syllogism

Deductive Reasoning Deductive Reasoning: The process of reasoning logically from given statements to a conclusion. Many people use deductive reasoning all the time.

Deductive Reasoning Because you don’t know the outcome will always be true with inductive reasoning, many times we use deductive reasoning to show that something will ALWAYS be true. With deductive reasoning, we start with a general case or cases, and use these to prove a specific case…which is the opposite of inductive reasoning.

The Parts of Deductive Reasoning Undefined terms are things that we accept but don’t formally define. A definition uses known words to describe a new word. A postulate is a statement that we assume to be universally true. A theorem is a statement that has been proven true using definitions, postulates, or other theorems.

Law of Detachment

Using Law of Detachment What can you conclude from the given statements? 1) If a student gets an A on a final exam, then the student will pass the course. Felicia got an A on her history exam. 2) If it is snowing, then the temperature is less than or equal to 32 degrees Fahrenheit. It is 20 degrees Fahrenheit.

Law of Syllogism Allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statement. Symbolic Form: If p  q and q  r are true statements, then p  r is a true statement. Example: If a number is prime, then it does not have repeated factors. If a number does not have repeated factors, then it is not a perfect square. Conclusion:

Using the Law of Syllogism If a number ends in 0, then its divisible by 10. If a number is divisible by 10, then it is divisible by 5. Conclusion: If a figure is a square, then the figure is a rectangle. If a figure is a rectangle, then the figure has four sides. Conclusion:

Using Both Laws If a river is more than 4000 mi. long, then it is longer than the Amazon. If a river is longer than the Amazon, then it is the longest river in the world. The Nile is 4132 mi. long. What can you conclude?

2.4 Homework: Mathxlforschool.com Due midnight.