2.4 Deductive Reasoning 2.4 Deductive Reasoning.

Slides:

Advertisements

Similar presentations

A Closer Look at Inductive vs. Deductive Reasoning.

Advertisements

A Closer Look at Inductive vs. Deductive Reasoning

Chapter 2 Geometric Reasoning

2.4 Deductive Reasoning HW: Lesson 2.4/ 1 – 10, 13.

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

Targets Use the Law of Detachment. Use the Law of Syllogism. Lesson 2-3: Deductive Reasoning TARGETS.

Using Deductive Reasoning to Verify Conjectures 2-3

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

Deductive Reasoning By. Mr. Kass.

Warm Up Make a conjecture based on the following information. For points A, B and C, AB = 2, BC = 3, and AC = 4. A, B, and C form an equilateral triangle.

Inductive & Deductive Reasoning

Section 2.3 Deductive Reasoning.

Using Deductive Reasoning to Verify Conjectures 2-3

Holt McDougal Geometry 2-1 Using Inductive Reasoning to Make Conjectures 2-1 Using Inductive Reasoning to Make Conjectures Holt Geometry Warm Up Warm Up.

Holt McDougal Geometry 2-3 Using Deductive Reasoning to Verify Conjectures Determine if each conjecture is true or false. If false, provide a counterexample.

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

Reasoning and Conditional Statements Advanced Geometry Deductive Reasoning Lesson 1.

Deductive Reasoning Chapter 2 Lesson 4.

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.

Thinking Mathematically Problem Solving and Critical Thinking.

Holt McDougal Geometry 2-3 Using Deductive Reasoning to Verify Conjectures Students will… Apply the Law of Detachment and the Law of Syllogism in logical.

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

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.

Section 2.3: Deductive Reasoning

Deductive and Inductive Reasoning

p qp q q pq p p  q ~p  ~q ~q  ~p q p September 17, 2014.

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.

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.

Do NOW: 1.) Solve 2(x – 15) = 30. Write a justification for each step. 2.) Find the next number in this sequence: 3, 5, 8, … How is the reasoning different.

2.1, 2.3, 2.4 Inductive and Deductive Reasoning and Biconditional Statements.

LG 1: Logic A Closer Look at Reasoning

Using Deductive Reasoning to Verify Conjectures 2-3

Deductive Reasoning, Postulates, and Proofs

2-3 Apply Deductive Reasoning

2-3 Deductive Reasoning Warm Up Lesson Presentation Lesson Quiz

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.

2.2 Inductive and Deductive Reasoning

02-2: Vocabulary inductive reasoning conjecture counterexample

Section 2-3: Deductive Reasoning

Inductive and Deductive Reasoning

Using Deductive Reasoning to Verify Conjectures 2-3

Using Deductive Reasoning to Verify Conjectures 2-3

2.2 Deductive Reasoning Objective:

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:

Vocabulary inductive reasoning conjecture counterexample

Using Deductive Reasoning to Verify Conjectures 2-3

Using Deductive Reasoning to Verify Conjectures 2-3

Using Deductive Reasoning to Verify Conjectures 2-3

Deductive Reasoning.

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

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

A Closer Look at Inductive vs. Deductive Reasoning

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.

1-6: Deductive Reasoning

Using Deductive Reasoning to Verify Conjectures 2-3

A Closer Look at Inductive vs. Deductive Reasoning

Using Deductive Reasoning to Verify Conjectures

Using Deductive Reasoning to Verify Conjectures 2-3

Using Deductive Reasoning to Verify Conjectures 2-3

Learning Target Students will be able to: Apply the Law of Detachment and the Law of Syllogism in logical reasoning.

Using Deductive Reasoning to Verify Conjectures 2-3

A Closer Look at Inductive vs. Deductive Reasoning

2-3 Apply Deductive Reasoning

Using Deductive Reasoning to Verify Conjectures 2-3

Consider the following TRUE conditional statement…

Presentation transcript:

2.4 Deductive Reasoning 2.4 Deductive Reasoning

Objectives: Use the Law of Detachment and Law of Syllogism. 2.4 Deductive Reasoning

Vocabulary: Deductive Reasoning Inductive Reasoning Law of Detachment Law of Syllogism 2.4 Deductive Reasoning

SOLVE IT! 2.4 Deductive Reasoning

Deductive vs. Inductive Reasoning The difference: inductive reasoning uses patterns to arrive at a conclusion (conjecture) deductive reasoning uses facts, rules, definitions or properties to arrive at a conclusion. 2.4 Deductive Reasoning

Deductive reasoning is the process of reasoning logically from given statements to a conclusion.

Examples of Inductive Reasoning Every quiz has been easy. Therefore, the test will be easy. The teacher used PowerPoint in the last few classes. Therefore, the teacher will use PowerPoint tomorrow. Every fall there have been hurricanes in the tropics. Therefore, there will be hurricanes in the tropics this coming fall. 2.4 Deductive Reasoning

Example of Deductive Reasoning The catalog states that all entering freshmen must take a mathematics placement test. An Example: You are an entering freshman. Conclusion: You will have to take a mathematics placement test. 2.4 Deductive Reasoning

Inductive or Deductive Reasoning? Geometry example… 60◦ x Triangle sum property – the sum of the angles of any triangle is always 180 degrees. Therefore, angle x = 30° Deductive Reasoning – conclusion is based on a property 2.4 Deductive Reasoning

Inductive or Deductive Reasoning? Geometry example… What comes next? Is there a rule? Colored triangle rotating 90° CW in the corners of the square Inductive Reasoning 2.4 Deductive Reasoning

2.4 Deductive Reasoning

2.4 Deductive Reasoning

Deductive Reasoning Is… Deductive reasoning is when you start from things you assume to be true, and draw conclusions that must be true if your assumptions are true. For Example All dogs have a tail. Buddy is a dog. Therefore Buddy has a tail. 2.4 Deductive Reasoning

How Can Deductive Reasoning Be Applied In School? Math Scott has a case of soda in his house since there are 13 cans of soda left I deduce that Scott has drank 11 cans of soda. English When I see ‘like’ in a sentence, I deduce that it is a simile. 2.4 Deductive Reasoning

Using laws and rules to make assumptions Science Using laws and rules to make assumptions The law of gravity means everything that goes up must come down I threw a baseball in the air That means the baseball must come down. Social Studies To be elected President you must obtain at least 270 electoral votes George Bush won 287 electoral votes Therefore George Bush is the President. 2.4 Deductive Reasoning

2.4 Deductive Reasoning

Law of Detachment: You can use this law to provide conclusions to statements. 2.4 Deductive Reasoning

If M is the midpoint of a segment, then it divides the segment into two congruent segments. Given: M is the midpoint of . You can conclude that M divides into two congruent segments, or 2.4 Deductive Reasoning

If an angle is obtuse, then it is not acute. is not obtuse. The converse of the assumption is not true, so It is not possible to conclude that is acute. 2.4 Deductive Reasoning

Law of Syllogism: You can use this law to state a conclusion from two true conditional statement. 2.4 Deductive Reasoning

If you practice your math, then you will get good grades. If a figures is a square, then the figure is a rectangle. If a figure is a rectangle, then the figure has four sides. Conclusion: if the figure is a square, then the figure has four side. If you practice your math, then you will get good grades. If you get good grades in math, then you will pass the class. Conclusion: if you practice your math, then you will pass the class. 2.4 Deductive Reasoning

Lesson Check: 2.4 Deductive Reasoning

Lesson Check: 2.4 Deductive Reasoning