Informal Approach Section 1.5. So far our “informal way”: Led to interesting and practical results Made simple constructions … but do not know how or.

Slides:

Advertisements

Similar presentations

Honors Geometry Section 4.6 (1) Conditions for Special Quadrilaterals

Advertisements

2.5 If-Then Statements and Deductive Reasoning

Geometry 2.3 Big Idea: Use Deductive Reasoning

MA/CSSE 473/474 How (not) to do an induction proof.

4.9 What Is Left To Prove? Pg. 30 Parts of Congruent Triangles.

Inductive Reasoning.  Reasoning based on patterns that you observe  Finding the next term in a sequence is a form of inductive reasoning.

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

Geometry Inductive Reasoning and Conjecturing Section 2.1.

1. Estimate the size of each angle below. Then determine if it is acute, right, obtuse, or straight. 170  30  90  100  180 

2.2 What’s the Relationship? Pg. 8 Complementary, Supplementary, and Vertical Angles.

Honors Geometry Section 1.0 Patterns and Inductive Reasoning

COORDINATE GEOMETRY PROOFS USE OF FORMULAS TO PROVE STATEMENTS ARE TRUE/NOT TRUE: Distance: d= Midpoint: midpoint= ( ) Slope: m =

SECTION 2-5 Angle Relationships. You have now experienced using inductive reasoning. So we will begin discovering geometric relationships using inductive.

Parallel and Perpendicular

Inductive Reasoning. The process of observing data, recognizing patterns and making generalizations about those patterns.

Proof using distance, midpoint, and slope

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

Geometry 27 January 2014 WARM UP 1) Complete Using Congruent Triangles handout 2) Place Khan video notes on top of group folder FINISHED? Work on Geometry.

Properties of Quadrilaterals

Conjectures that lead to Theorems 2.5

2.2 What’s the Relationship? Pg. 8 Complementary, Supplementary, and Vertical Angles.

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

Deductive Reasoning Chapter 2 Lesson 4.

Reasoning Strategies Goal: To be able to identify a deductive or inductive reasoning strategy State the hypothesis and conclusion of deductive statements.

Chapter 2 Connecting Reasoning and Proof

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.

Ch. 6 Review Classwork. 1. Copy and complete the chart. Just write the names of the quadrilaterals.

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

DEDUCTIVE VS. INDUCTIVE REASONING. Problem Solving Logic – The science of correct reasoning. Reasoning – The drawing of inferences or conclusions from.

Thinking Mathematically Problem Solving and Critical Thinking.

PRE-ALGEBRA. Lesson 1-7 Warm-Up PRE-ALGEBRA Inductive Reasoning (1-7) inductive reasoning: making judgements or drawing conclusions based on patterns.

1.2 Inductive Reasoning. Inductive Reasoning If you were to see dark, towering clouds approaching what would you do? Why?

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.

Ways of proving a quadrilaterals are parallelograms Section 5-2.

The Scientific Method: How to solve just about anything.

Postulates and Theorems Relating Points, Lines, and Planes

Lesson 1.2 Inductive Reasoning Pages Observe Look for patterns Develop a hypothesis (or conjecture) Test your hypothesis.

Megan FrantzOkemos High School Math Instructor.  Use inductive reasoning to identify patterns and make conjectures.  Determine if a conjecture is true.

Higher / Int.2 Philosophy 12. Our Learning  Fallacy Reminder  Summary following Homework NAB  Class NAB.

Use Properties of Parallelograms

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,

Using the Distance Formula in Coordinate Geometry Proofs.

quadrilateral consecutive congruent perpendicular = 90 o congruent bisect.

Chapter 9 Circles Define a circle and a sphere.

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

A rhombus is a parallelogram with __ ________________ ___________. A rectangle is a parallelogram with ___ __________ ____________. A square is a parallelogram.

LG 1: Logic A Closer Look at Reasoning

Lesson 1-7 Inductive Reasoning. Inductive Reasoning – making conclusions based on patterns you observe. Conjecture – conclusion you reach by inductive.

(Proof By) Induction Recursion

Section 2-4 Deductive Reasoning.

Constructing specific quads

Section 8.4 Notes.

2-1 Patterns and Inductive Reasoning

Section 6.3 Proving Quadrilaterals are parallelograms

CST 24 – Logic.

6.5 Rhombi and Squares.

The Scientific Method.

Five step procedure for drawing conclusions.

Section 24.4: Conditions for Rectangles, Rhombuses, and Squares

Section 24.4: Conditions for Rectangles, Rhombuses, and Squares

2-1 Inductive Reasoning.

Section 6.3 Proving Quadrilaterals are parallelograms

Tools and methods in biology

Inductive Reasoning and Conjecture, and Logic

Proving a quadrilateral is a parallelogram

Constructing specific quads

Chapter 5: Quadrilaterals

1-4 Inductive reasoning Homework: 4-6, 10-14,

1-5 Conditional statements 1-6 deductive reasoning

Presentation transcript:

Informal Approach Section 1.5

So far our “informal way”: Led to interesting and practical results Made simple constructions … but do not know how or why they work Guessed conclusions based on appearances … not always certain they are true This is unsatisfactory … we have no basis to know if conclusions are correct!!!

Like Egyptians 4,000 years ago: Accumulation of rules and results based on trial and error Satisfied with ideas that appeared to be useful … without questioning why they might (or might not) be true

Ancient Egyptians: Formula for area of fields Area = ¼(a + c)(b + d) Based on: area of quadrilateral = product of average lengths of opposite sides b ac d L L WW Only works for a rectangle (overstates all other quads)

Leads us to: Critical thinking Careful analysis Provocative problems (bisect, trisect)

Leads to questions: How to prove something is impossible? How to tell the difference between something that is exactly right and almost right? How to prove something?

Types of Reasoning: Inductive Reasoning: Drawing conclusions from a limited set of observations. Deductive Reasoning: Use of logic to draw conclusions from statements already accepted as true.

Homework: Read pages 6 and 30 – 31 Do page 31 #1 – 15 (need compass and protractor)