2-3 Conditional Statements

Slides:

Advertisements

Similar presentations

9/2/2008 Warm Up Complete the conjecture by looking for a pattern in the diagram below. The number of sides of a polygon that has n vertices is________________.

Advertisements

Conditional Statements

When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. Inductive reasoning is the process.

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

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

Conditional Statements and Logic 2.2 Ms. Verdino.

Conditional Statements

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

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

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,

Geometry CH 4-1 Using Logical Reasoning Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

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

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.

Review Complete the chart: pq Conditional p  q Converse _  _ TT TF FT FF.

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

Conditional Statements

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

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.

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.

Unit 01 – Lesson 07 – Conditional Statements

Conditional Statements and the Converse Geometry Unit 11, Day 7 Ms. Reed.

Section 2.2 Analyze Conditional Statements. What is an if-then statement? If-then statements can be used to clarify statements that may seem confusing.

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:

2-2 Conditional Statements Objectives: To recognize conditional statements and their parts To write converses, inverses, and contrapositives of conditionals.

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

2.2 Conditional Statements Objective: Students will analyze statements in if-then form and write the converse, inverse, and contrapositive of if-then statements.

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.

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

2.2 – Analyze Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

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

Lesson 2-3: Conditional Statements

A logic statement written in if-then form.

2-2 Conditional Statements

Conditional Statements

Conditional Statements

Conditional Statements

Opening hexagon A _____________________ has six sides.

Conditional Statements

Conditional Statements

Conditional Statements

Chapter 2.2 Notes: Analyze Conditional Statements

Lesson 2 – 3 Conditional Statements

More Conditional Statements

Conditional Statements

Logic and Reasoning.

Angles, Angle Pairs, Conditionals, Inductive and Deductive Reasoning

Conditional Statements

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

Conditional Statements

Conditional Statements

Conditional Statements

Different Forms of Conditional Statements

2-2: Conditional Statements

Presentation transcript:

2-3 Conditional Statements Conditional Statement: A statement that can be written in if-then form. If-Then Statement: Written in the form if p, then q. (p q) Hypothesis: The phrase immediately following the word if. Conclusion: The phrase immediately following the word then.

Example #1 Identify the hypothesis and conclusion. A) If a polygon has six sides, then it is a hexagon. B) Another performance will be scheduled if the first one is sold out. Some conditional statements are written without the if and then. Example #2: Identify the hypothesis and conclusion. Then write each statement in if-then form. A) An angle formed by perpendicular lines is a right angle. If an angle is formed by perpendicular lines, then it is a right angle. B) A cheetah has nonretractile claws. If a cat is a cheetah then it has nonretractile claws.

Truth Tables using if-then p q pq T F

Example #3: Determine the truth value of the following statement for the set of conditions. If you get 100% on your test, then your teacher will give you an A. A) You get 98%; your teacher gives you an A. Hypothesis is false, the conclusion is true…therefore the statement is true. B) You get 85%; your teacher gives you a B. Hypothesis is false, but we can not say that the entire statement is false…therefore the statement is true. C) You get 100%, your teacher gives you a B. Hypothesis is true, but the conclusion is false. Therefore the statement is false.

Vocabulary Related Conditionals: Other statements based on a given conditional statement. Conditional: Given hypothesis and conclusion. p  q. Converse: Exchanging the hypothesis and conclusion of the conditional. q p Inverse: Negating both hypothesis and conclusion of the conditional. ~p~q Contrapositive: Negating both the hypothesis and conclusion of the converse statement. ~q ~p Logically Equivalent: Statements with the same truth values.

Truth Table for all related conditionals p q Conditional pq Converse qp Inverse ~p~q Contrapositive ~q~p T F

Example #4 Write the converse, inverse, and contrapositive of the following statement. Determine whether the statement is true or false. If the statement is false, give a counterexample. Vertical angles are congruent. Conditional: If a pair of angles are vertical, then they are congruent. True Converse: If a pair of angles are congruent, then they are vertical. False – counterexample: two right angles adjacent to one another are congruent but are not vertical. Inverse: If a pair of angles are not vertical, then they are not congruent. False – counterexample: linear pair formed by two right angles are congruent but not vertical. Contrapositive: If a pair of angles are not congruent, then they are not vertical. True