Welcome to Proofs!. The Basics Structure: Given information (sometimes assumption) Step-by-step reasoning Conclusion Types of reasoning: Inductive-use.

Slides:

Advertisements

Similar presentations

Chapter 2 Review Lessons 2-1 through 2-6.

Advertisements

Geometry Chapter 2 Terms.

Chapter 2 Geometric Reasoning

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

Conditional Statements Conditional - Conditionals are formed by joining two statements with the words if and then: If p, then q. The if-statement is the.

Inductive Reasoning and Conjecture “Proofs”

Conditional Statements youtube. com/watch SOL: G.1a SEC: 2.3.

Unit 2 Reasoning & Proof.

Welcome to Interactive Chalkboard 2.3 Conditional Statements.

Holt Geometry 2-1 Using Inductive Reasoning to Make Conjectures Welcome to our Unit on Logic. Over the next three days, you will be learning the basics.

2-1 Inductive Reasoning & Conjecture

Chapter 2.3 Conditional Statements. Conditional Statement.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–2) Then/Now New Vocabulary Key Concept: Conditional Statement Example 1: Identify the Hypothesis.

conditional statement contrapositive

2.3 Analyze Conditional Statements. Objectives Analyze statements in if-then form. Analyze statements in if-then form. Write the converse, inverse, and.

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.

Chapter Two Emma Risa Haley Kaitlin. 2.1 Inductive reasoning: find a pattern in specific cases and then write a conjecture Conjecture: unproven statement.

2-3 Conditional Statements You used logic and Venn diagrams to determine truth values of negations, conjunctions, and disjunctions. Analyze statements.

$100 $200 $300 $400 $500 $200 $300 $400 $500 Inductive Reasoning and Logic Conditional Statements Angle and Segment Addition Deductive Reasoning Postulates.

Lesson 2-3 Conditional Statements. 5-Minute Check on Lesson 2-2 Transparency 2-3 Use the following statements to write a compound statement for each conjunction.

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

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 

2-1 Inductive Reasoning & Conjecture INDUCTIVE REASONING is reasoning that uses a number of specific examples to arrive at a conclusion When you assume.

Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

INDUCTIVE REASONING AND CONJECTURE. DEFINITIONS Conjecture: a best guess based on known information. Inductive Reasoning: using specific examples to arrive.

1. If p  q is the conditional, then its converse is ?. a. q  pb. ~q  pc. ~q  ~pd. q  ~p 2. Which statement is always true? a. x = xb. x = 2c. x =

Conditional Statements

Conditional Statements

Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

Conjecture: an educated guess

Deductive Structure Statements of Logic. The Structure.

Chapter 2 Reasoning and Proof. 2.1 Inductive Reasoning and Conjecture Conjecture- an educated guess based on known information Inductive reasoning- reasoning.

2.3 Conditional Statements 0 Conditional statement- a statement that can be written in if-then form.

Splash Screen Today in Geometry Lesson 2.1: Inductive Reasoning Lesson 2.2: Analyze conditional statements.

They are easier than Geometry ones!!. PROOFS The “GIVEN” is always written first –It is a “GIMME” The “PROVE” should be your last line Make a two column.

Reasoning, Conditionals, and Postulates Sections 2-1, 2-3, 2-5.

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

Geometry Review Jeopardy. Review Jeopardy Rules On a teams’ first pick they must pick a questions worth 20 points or LESS On a teams’ second pick they.

Reasoning and Proof Chapter – Conditional Statements Conditional statements – If, then form If – hypothesis Then – conclusion Negation of a statement-

1 Conditional Statements “IF-THEN”. If- Then Statements If- Then Statements are commonly used in everyday life. Advertisement might say: “If you buy our.

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:

Transparency 2 Review: Lesson 2-1 Mini-Quiz. Class Greeting.

2.3 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Apply Deductive Reasoning.

Inductive and Deductive Reasoning Reasoning is used in mathematics, science, and everyday life. When you reach a conclusion, called a generalization,

Inductive Reasoning Inductive Reasoning: The process of using examples, patterns or specific observations to form a conclusion, conjecture, or generalization.

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

Objective - To use properties of numbers in proofs. Logical Reasoning Deductive ReasoningInductive Reasoning - process of demonstrating that the validity.

1. Write the converse, inverse, and contrapositive of. “If

Reasoning and Proof Unit 2.

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.

Reasoning Proof and Chapter 2 If ….., then what?

CST 24 – Logic.

Y. Davis Geometry Notes Chapter 2.

2.1: Patterns and Inductive Reasoning

2-4 Deductive Reasoning Ms. Andrejko.

Make a conjecture about the next item in the sequence. 1, 4, 9, 16, 25

Conditional Statements

2.1 Patterns and Inductive Reasoning

SWBAT analyze statements in if-then form.

Chapter 2 Reasoning and Proof.

1. Write the converse, inverse, and contrapositive of. “If

1. Write the converse, inverse, and contrapositive of the conditional below and determine the truth value for each. “If the measure of an angle is less.

Prove Statements about Segments and Angles

Inductive Reasoning and Conjecture

Chapter 2 Reasoning and Proof.

Lesson 2-R Chapter 2 Review.

Presentation transcript:

Welcome to Proofs!

The Basics Structure: Given information (sometimes assumption) Step-by-step reasoning Conclusion Types of reasoning: Inductive-use a number of specific examples to arrive at conclusion (called a “conjecture”) Deductive- use facts, rules, definitions, or properties to reach a conclusion

Example of inductive reasoning Write a conjecture that describes the pattern. Movie show times: 8:30am, 9:45am, 11:00am, 12:15am… The show time is 1 hour and 15 minutes greater than the previous show. The next show time will be 12:15am + 1:15= 1:30pm. The examples of movie times showed us a pattern, and we were able to come to a conclusion based on that pattern.

Example of deductive reasoning At Fumio’s school if you are late 5 times, you will receive a detention. Fumio has been late to school 5 times; therefore he will receive a detention.

Are the following examples of inductive or deductive reasoning? Discuss with your partner. 1.) Every Wednesday Lucy’s mother calls. Today is Wednesday, so Lucy concludes that her mother will call. 2.) A person must have a membership to work out at a gym. Jesse is working out at a gym. I conclude that Jesse has a membership to the gym. 3.) A dental assistant notices a patient has never been on time for an appt. She concludes the patient will be late for her next appt. 4.) If Eduardo decides to go to a concert tonight, he will miss football practice. Tonight, Eduardo went to a concert, so he missed football practice.

Conditional Statements (“If-Then” statements) Uses a hypothesis-conclusion format Example 1: If the forecast is rain (hypothesis), then I will take an umbrella (conclusion) Example 2: A number is divisible by 10 (conclusion) if its last digit is 0 (hypothesis) If p q If q p (converse) If –p -q (inverse) If –q -p (contrapositive)

If-Then Statements With your partner, determine what the hypothesis and conclusion are of each statement. Also, determine if the converse is true. If a polygon has 6 sides, then it is a hexagon. Tamika will advance to the next level of play if she completes the maze in her computer game. A five-sided polygon is a pentagon. An angle that measures 45° is an acute angle.

Who remembers the book If You Give a Mouse a Cookie? 2.5 POSTULATES AND PARAGRAPH PROOFS

 Objective: I will be able to… -Prove relationships between points, lines, and planes using deductive reasoning and paragraph proofs 2.5 POSTULATES AND PARAGRAPH PROOFS

The proof process

We just proved this!

Try one with your partner!

2.6 Algebraic proof A proof that is made up of a series of algebraic statements. Reasoning uses properties of real numbers (addition, subtraction, multiplication, division, reflexive, distributive, substitution, etc.)

2.7 Proving segment relationships C F G E D