Sec. 2.3: Apply Deductive Reasoning

Slides:

Advertisements

Similar presentations

Sec.2-3 Deductive Reasoning

Advertisements

2.5 If-Then Statements and Deductive Reasoning

Geometry 2.3 Big Idea: Use Deductive Reasoning

Deductive Reasoning. Objectives I can identify an example of inductive reasoning. I can give an example of inductive reasoning. I can identify an example.

2.5 - I F -T HEN S TATEMENTS AND D EDUCTIVE R EASONING Homework #6.

Lesson 2.3 p. 87 Deductive Reasoning Goals: to use symbolic notation to apply the laws of logic.

4.3 Warm Up Find the distance between the points. Then find the midpoint between the points. (5, 2), (3, 8) (7, -1), (-5, 3) (-9, -5), (7, -14)

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

Chapter 2: Geometric Reasoning

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.

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.

2.5 Proofs Segments and Angles

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?

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

Deductive Reasoning Chapter 2 Lesson 4.

 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.

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

Section 2-2: Conditional Statements. Conditional A statement that can be written in If-then form symbol: If p —>, then q.

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.

Ch. 2.3 Apply Deductive Reasoning

Section 2.3: Deductive Reasoning

Section 2.2 Inductive and Deductive Reasoning. Definition: Conjecture an unproven statement that is based on observations or given information.

Warm up… Write the converse, inverse, and contrapositive. Whole numbers that end in zero are even. Write as a biconditional. The whole numbers are the.

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

3/15/ : Deductive Reasoning1 Expectations: L3.1.1: Distinguish between inductive and deductive reasoning, identifying and providing examples of each.

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

Name vertical angles and linear pairs. Name a pair of complementary angles and a pair of supplementary angles.

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:

LG 1: Logic A Closer Look at Reasoning

Reasoning in Algebra & Deductive Reasoning (Review) Chapter 2 Section 5.

Using Deductive Reasoning to Verify Conjectures 2-3

2-4 Deductive Reasoning Objective:

Reasoning and Proof Unit 2.

Deductive Reasoning, Postulates, and Proofs

2-3 Apply Deductive Reasoning

2.2 Inductive and Deductive Reasoning

Chapter 2 Review Geometric Reasoning.

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

Apply Deductive Reasoning

} { Using facts, definitions, accepted properties and the

Applying Deductive Reasoning

2.4 Deductive Reasoning.

Warmup Definition: Perpendicular Lines—

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.

2-3 Deductive Reasoning Objectives:

Drawing and Supporting Conclusions

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

Section 3-6 Inductive Reasoning.

2-3 Apply Deductive Reasoning

Angles, Angle Pairs, Conditionals, Inductive and Deductive Reasoning

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

Chapter 2 Reasoning and Proof.

Presentation transcript:

Sec. 2.3: Apply Deductive Reasoning Deductive Reasoning uses facts, definitions, accepted properties, and the laws of logic to form a logical argument.

Laws of Logic There are two laws of logic that help us draw logical conclusions from information given. The Law of Detachment and the Law of Syllogism.

Law of Detachment If the hypothesis (condition) of a true conditional statement is true, then the conclusion is also true. Ex. It is true that if you have a valid California drivers license, then you are allowed to drive in California. If you know Sam has a California drivers license, what can you conclude?

Law of Syllogism If you have two true conditional statements where the conclusion of the first is the hypothesis of the second, then you can conclude the hypothesis of the first will result in the conclusion of the second. If “p”, then “q” is true, and if “q”, then “r” is true, then you can conclude that if “p”, then “r”.

Syllogism Example Given: If two angles are a linear pair, then they are supplementary. If two angles are supplementary, then their measures add up to 180 degrees Using the Law of Syllogism we can logically conclude that “if two angles are a linear pair, then their measures add up to 180 degrees.”