MM1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive. BY: BETH MATHIS Terry Marshall Jr.

Slides:

Advertisements

Similar presentations

Geometry 2.2 Big Idea: Analyze Conditional Statements

Advertisements

Conditional Statements Geometry Chapter 2, Section 1.

Conditional Statements

 Writing conditionals  Using definitions as conditional statements  Writing biconditionals  Making truth tables.

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.

Conditional Statements

2.2 Conditional Statements Goal: Students will be able:  To recognize conditional statements and their parts.  To write converses, inverses, and contrapositives.

2.2 Analyzing Conditional Statements. Conditional Statements: Conditional Statement (In “If-Then” form): “If it is a bird, then it has feathers.” Ex.

2-2 Conditional Statements

Warm Up Determine if each statement is true or false. 1. The measure of an obtuse angle is less than 90°. 2. All perfect-square numbers are positive. 3.

Holt Geometry 2-2 Conditional Statements Warm Up : Photographers and Cannibals Three National Geographic photographers and three cannibals are traveling.

Conditional Statements

2.1 Conditional Statements Goals Recognize a conditional statement Write postulates about points, lines and planes.

10/21/2015Geometry1 Section 2.1 Conditional Statements.

10/21/2015Geometry1 Conditional Statements. 10/21/2015Geometry2 Goals Recognize and analyze a conditional statement Write postulates about points, lines,

Conditional Statements Conditional Statement: “If, then” format. Converse: “Flipping the Logic” –Still “if, then” format, but we switch the hypothesis.

Learning Targets I can recognize conditional statements and their parts. I can write the converse of conditional statements. 6/1/2016Geometry4.

Logic and Reasoning. Identify the hypothesis and conclusion of each conditional. Example 1: Identifying the Parts of a Conditional Statement A.If today.

Wednesday, October 24 th Aim: In what other ways can we potentially change the truth value of a conditional statement? Do Now: Write a TRUE conditional.

Over Lesson 2–2 5-Minute Check 1 A.True; 12 + (–4) = 8, and a triangle has four sides. B.True; 12 + (–4)  8, and a triangle has four sides. C.False; 12.

Conditional Statements. Standards/Objectives: Students will learn and apply geometric concepts. Objectives: –Recognize and analyze a conditional statement.

Conditional Statements Lesson 2-1. Conditional Statements have two parts: Hypothesis ( denoted by p) and Conclusion ( denoted by q)

Conditional Statements Learning Target: I can write converses, inverses, and contrapositives of conditionals.

2.1 Conditional Statements GOAL 1 Recognize and analyze a conditional statement. GOAL 2 Write postulates about points, lines, and planes using conditional.

Conditional Statements

Section 2-2: Biconditional and Definitions TPI 32C: Use inductive and deductive reasoning to make conjectures Objectives: Write the inverse and contrapositive.

Recognizing Conditional Statements If it is noon in Georgia, then it is 9 A.M. in California. hypothesis conclusion In this lesson you will study a type.

Unit 2 Part 1 Conditional, Converse, Inverse, and Contra- Positive Statements.

Section 2.2 Conditional Statements 1 Goals Recognize and analyze a conditional statement Write postulates about points, lines, and planes using conditional.

MMiG2 b – Converses and conditional statements

Chapter Conditional statements. * Identify, write, and analyze the truth value of conditional statements. * Write the inverse, converse, and contrapositive.

Inductive and Deductive Reasoning. Notecard 30 Definition: Conjecture: an unproven statement that is based on observations or given information.

Chapter 2.2 Notes: Analyze Conditional Statements Goal: You will write definitions as conditional statements.

Section 2-1 Conditional Statements. Conditional statements Have two parts: 1. Hypothesis (p) 2. Conclusion (q)

Conditional Statements Section 2-3 Conditional Statements If-then statements are called conditional statements. The portion of the sentence following.

Logic and Reasoning Conditional Statements. Logic The use and study of valid reasoning. When studying mathematics it is important to have the ability.

MM1G2.b. Understand and use the relationships among the statement and it converse inverse and contrapositive. Destiny and Scott.

Conditional Statements Geometry Chapter 2, Section 1.

2-3 Conditional Statements- Related What are the three related conditional statements? How are the three related conditional statements made?

2.3 CONDITIONAL STATEMENTS Geometry R/H. A Conditional statement is a statement that can be written in the form: If P, then Q. The hypothesis is the P.

Recall Section 2-3: Biconditionals & Definitions Objectives:

2.1 Conditional Statements Goal 1: Recognizing Conditional Statements Goal 2: Using Point, Line, and Plane Postulates CAS 1,3.

2-1 Conditional Statements GOALS 1. Recognize and analyze a conditional statement. 2. Write postulates about points, lines, and planes using conditional.

By phrasing a conjecture as an if-then statement, you can quickly identify its hypothesis and conclusion.

Holt McDougal Geometry 2-2 Conditional Statements 2-2 Conditional Statements Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson.

Section 2.1 Geometric Statements. Definitions: Conditionals, Hypothesis, & Conclusions: A conditional statement is a logical statement that has two parts:

Inductive and Deductive Reasoning. Notecard 29 Definition: Conjecture: an unproven statement that is based on observations. You use inductive reasoning.

If-then statements April 4, What is an if-then statement? One of the postulates we looked at earlier stated: If B is between A and C, then AB +

Lesson 2-1 Conditional Statements 1 Lesson 2-3 Conditional Statements.

Inductive and Deductive Reasoning. Notecard 30 Definition: Conjecture: an unproven statement that is based on observations or given information.

Section 2.2 Homework Quiz Question Put the following Conditional Statement into If Then Form: All birds have feathers.

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

Section 2.1 Conditional Statements Standards #1&3 Wednesday, July 06, 2016Wednesday, July 06, 2016Wednesday, July 06, 2016Wednesday, July 06, 2016.

Conditional Statements

Objectives Identify, write, and analyze the truth value of conditional statements. Write the inverse, converse, and contrapositive of a conditional statement.

2.1 Conditional Statements

2-1 Vocabulary conditional statement hypothesis/conclusion

Objectives Identify, write, and analyze the truth value of conditional statements. Write the inverse, converse, and contrapositive of a conditional statement.

If-Then Statements/Converses

Conditional Statements

Warmup State whether each sentence is true or false.

Conditional Statements

Conditional Statements

Logical Sequencing & Conditional Statements

Conditional Statements

Logic and Reasoning.

Math Humor Teacher: Which month has 28 days? Student: All of them!!

Interpreting Truth tables (biconditional statements)

2-2: Conditional Statements

Presentation transcript:

MM1G2.b. Understand and use the relationships among a statement and its converse, inverse, and contrapositive. BY: BETH MATHIS Terry Marshall Jr.

 Using relationships among a statements and their converse, inverse, and contrapositive.  We need to be able to write and recognize converse,inverse, and contrapostive.

 Statement: a sentence that is either true or false, but not both  Example that is a statement: A triangle has three sides.  Example that is not a statement: Close the door.

 Conditional Statement: a logical statement with two parts usually in “if-then” form  It has two parts: the hypothesis (“if” part) and the conclusion (“then” part)

ConditionalIf p, then q.Original InverseIf not p, then not q.Negate ConverseIf q, then p.Switch ContrapositiveIf not q, then not p. Switch and Negate

 For a conditional statement to be true, that means that whenever the hypothesis is true, the conclusion is true also, with no exceptions! So, if there is even ONE exception, then you say it’s false! If you can come up with an exception that would be called a counterexample.  **A good way to remember that converse means to switch is to think about “converse” shoes switching back and forth when you are walking.

 If a polygon has four sides, then it is a quadrilateral. (true)  What is the hypothesis? A polygon has four sides What is the conclusion? It is a quadrilateral  Inverse(not): If a polygon does not have four sides, then it is not a quadrilateral. (true)  Converse(switch): If a polygon is a quadrilateral, then it has four sides. (true)  Contrapositive(switch and not): If a polygon is not a quadrilateral, then it does not have four sides. (true)

 Example: If it is a dog, then it is an animal. (true)  What is the hypothesis? It is a dog.What is the conclusion? It is a an animal.  Inverse(not): If it is not a dog, then it is not an animal. (false)  Counterexample: A cat is not a dog which makes the hypothesis true, but it is an animal which makes the conclusion false.  Converse(switch): If is an animal, then it is a dog. (false)  Counterexample: A cat is an animal which makes the hypothesis true, but it is not a dog which makes the conclusion false.  Contrapositive(switch and not): If it is not an animal, then it is not a dog. (true)

 When two statements are both true or both false, they are called equivalent statements.

 ***The contrapositive is always logically equivalent to the original statement- meaning that the conditional statement is true, the contrapositive must also be true.  A biconditional statement has the words “if and only if” instead of just “if”.  You may write a biconditional statement only if the statement and it’s converse are both true.

 Statement: If a whole number is even then it divisible by two. (true)  Converse: If a whole number is divisible by two, then it is even. (true)  Biconditional: A whole number is even if and only if it is divisible by two.  Example: Statement: If you are in Mrs. Kesler’s class then you are a student. (true)  Converse: If you are a student then you are in Mrs. Kesler ’s class. (false)  Biconditional: I can’t write a biconditional because the converse is false – not all students are in Mrs. Kesler’s class.