Unit 2 Reasoning and Proof “One meets his destiny often in the road he takes to avoid it.” ~ French Proverb.

Slides:

Advertisements

Similar presentations

2.1 If-Then Statements; Converses

Advertisements

Bell Work 1) Write the statement in “If/Then” Form. Then write the inverse, converse, and contrapositive: a) A linear pair of angles is supplementary.

Notes on Logic Continued

Use the following conditional for Exercises 1–3. If a circle’s radius is 2 m, then its diameter is 4 m. 1.Identify the hypothesis and conclusion. Hypothesis:

Do Now: 1.Copy Down HW. 2.Describe the pattern, then find the next two numbers in the pattern: 3, 12, 48, 192, …

Conditional Statements

Jeopardy Chapter 2.

10/21/2015Geometry1 Section 2.1 Conditional Statements.

Bell Work Conditional: If the car is running, then it has fuel 1) Write the converse 2) Write the “opposite” statement of the conditional 3) Write the.

2.2 Definition and Biconditional Statements Use definitions and biconditional statements.

Ex. 1 Identifying Hypothesis and Conclusion A conditional is an If, then statement Made of two parts Hypothesis and conclusion Hypothesis follows the.

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

Chapter 2 Review. Conditional statements have a IF and a THEN. 2 Hypothesis Conclusion.

Section 2-2 Biconditional Statements. Biconditional statement a statement that contains the phrase “if and only if”. Equivalent to a conditional statement.

Section 2-1 Using Deductive Reasoning. If/then statements Called conditional statements or simply conditionals. Have a hypothesis (p) and a conclusion.

Boyd/Usilton. Conditional If-then statement that contains a hypothesis (p) and a conclusion (q). Hypothesis(p): The part of the conditional following.

Inductive Reasoning and Conditional Statements

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.

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

Statements that are Conditional with a hypothesis and a conclusion. The If part of the statement is the Hypothesis, and the Then part of the statement.

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

2.2.1 Analyze Conditional Statements and Proof Chapter 2: Reasoning and Proof.

Section 2.2 Analyze Conditional Statements. Homework Pg 82 #3-5, 11-15,

Warm up 1.Re-write the following statements as an if-then statement. 2.State the converse of the statement. a.The midpoint of a segment is a point that.

Day 3. Warm Up Find the distance and midpoint between the two points below.

Chapter 2 Section 2 Biconditionals and Definitions.

1 If-then Statements “If-then statements” are also called “Conditional Statements” or just “Conditionals” “If-then statements” are also called “Conditional.

Section 2-2: Biconditionals and Definitions. Conditional: If two angles have the same measure, then the angles are congruent. Converse: If two angles.

Chapter 2: Reasoning & Proof 2.2 Biconditionals & Definitions.

 If an integer ends with 0, then the integer is divisible by 2.  What is the truth value of the above conditional?  What is the converse?  What is.

Inductive and Deductive Reasoning. Definitions: Conditionals, Hypothesis, & Conclusions: A conditional statement is a logical statement that has two parts:

Section 2.4 Conditional Statements. The word “logic” comes from the Greek word logikos, which means “reasoning.” We will be studying one basic type of.

 When a conditional and its converse are both true, we combine them to make a biconditional.  Example:  Biconditional – An angle is right if and only.

Geometry Review 1 st Quarter Definitions Theorems Parts of Proofs Parts of Proofs.

2.3 Biconditionals and Definitions 10/8/12 A biconditional is a single true statement that combines a true conditional and its true converse. You can join.

Conditional Statments. Warm Up What is the fourth point of plane XUR Name the intersection of planes QUV and QTX Are point U and S collinear?

2.1 CONDITIONAL STATEMENTS 10/2. Learning Targets I can find the truth value given a conditional and a converse I can rewrite a statement as a conditional.

Chapter 2 Section 2.1 – Conditional Statements Objectives: To recognize conditional statements To write converses of conditional statements.

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

Reasoning and Proof DAY 3: 2.3 Biconditional Statements.

2-3 Biconditionals and Definitions Objective: To write biconditionals and recognize good definitions.

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

2.1, 2.2 and 5.4: Statements and Reasoning. Conditional is an if-then statement that contains two parts. The part following the if is the Hypothesis.

2-1 Conditional Statements M11.B.2 Objectives: 1) To recognize conditional statements. 2) To write converses of conditional statements.

2-3 Biconditionals and Defintions. Biconditional- a statement that is the combination of a conditional statement and its converse. If the truth value.

CONDITIONAL STATEMENTS Section 2-1. Objectives  To recognize conditional statements.  To write converses of conditional statements.

CONDITIONAL STATEMENTS If-Then Statements Section 2.2.

Overview of Sections 1.1, Sections 1.1, 2.1, 2,2 and 2.3 Combined like Transformers!

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

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.

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

Conditional Statements A conditional statement has two parts, the hypothesis and the conclusion. Written in if-then form: If it is Saturday, then it is.

2.2 Definitions and Biconditional Statements GOAL 1 Recognize and use definitionsGOAL 2 Recognize and use biconditional statements. What you should learn.

Bell Work Find the hypothesis and conclusion 1) If the class behaves, then Mr. Liu will give all the students 5 point extra credit Find the converse 2)

Conditional & Biconditional Statements Chapter 2 Section 2 1.

Conditional & Biconditional Statements Chapter 2 Section 4.

2-1 CONDITIONAL STATEMENTS

Chapter 2: Reasoning & Proof Conditionals, Biconditionals, & Deductive Reasoning.

Chapter 2 Deductive Reasoning

Conditional Statements

Conditional Statements

Definitions and Biconditional Statements

Conditional Statements

2.2 Definitions and Biconditional Statements

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

Conditional Statements

Section 2.2 Definitions and Biconditional Statement

G7 Conditional Statements

Proving Lines Parallel

Presentation transcript:

Unit 2 Reasoning and Proof “One meets his destiny often in the road he takes to avoid it.” ~ French Proverb

What You’ll Learn Next in this Chapter… (2.1/2.2) How to write special types of statements…conditionals, biconditionals, definitions, etc...

Conditional is an if-then statement that contains two parts. The part following the if is the Hypothesis. The part following then is the Conclusion. Example 1: If you live in a country that borders the United States, then you live in Canada. Hypothesis: You live in a country that borders the United States. Conclusion: You live in Canada. (2.1) Conditional Statements

Conditional is an if-then statement that contains two parts. The part following the if is the Hypothesis. The part following then is the Conclusion. Example 2: If two lines are parallel, then the lines are coplanar. (2.1) Conditional Statements Hypothesis: Two lines are parallel. Conclusion: The lines are coplanar.

Conditional is an if-then statement that contains two parts. The part following the if is the Hypothesis. The part following then is the Conclusion. Example 3: Write the statement as a conditional. An acute angle measures less than 90 degrees. (2.1) Conditional Statements Hypothesis : An angle is acute First part of the Conditional: “If an angle is acute” Conclusion : It measures less than 90 degrees Second part of the Conditional: “then it measures less than 90 degrees.” Conditional Statement: If an angle is acute, then it measures less than 90 degrees.

Conditional is an if-then statement that contains two parts. The part following the if is the Hypothesis. The part following then is the Conclusion. Example 4: Write a counterexample to make the conditional false. If x 2 > 0, then x > 0. The counterexample for the conditional is when the hypothesis is true and the conclusion is false. (2.1) Conditional Statements

Converse of a conditional switches the hypothesis and the conclusion. Example 1: Writing the converse of the conditional. Conditional: If two lines intersect to form right angles, then they are perpendicular. Converse: If two lines are perpendicular, then they intersect to form right angles. (2.1) Converse

Converse of a conditional switches the hypothesis and the conclusion. Example 2: Writing the converse of the conditional. Conditional: If x = 9, then x + 3 = 12 Converse: (2.1) Converse If x + 3 = 12, then x = 9

Converse of a conditional switches the hypothesis and the conclusion. Example 3: Write the converse of the conditional, determine the truth value of each. Conditional: If a 2 = 25, then a = 5 Converse: (2.1) Converse If a = 5, then a 2 = 25

Biconditionals When a conditional and its converse are true, you can combine them as a true biconditional. You can combine them by using the phrase if and only if. Example 1: Consider the conditional. Write its converse. If they are both true, combine the statements as a biconditional. Conditional: If two angles have the same measure, then the angles are congruent. Converse: Biconditional: (2.2) Biconditionals If two angles are congruent, then the angles have the same measure. Two angles have the same measure if and only if the angles are congruent.

Biconditionals When a conditional and its converse are true, you can combine them as a true biconditional. You can combine them by using the phrase if and only if. Example 2: Write the two statements that form each biconditional. You live in Washington, D.C. if and only if you live in the capital of the United States. (2.2) Biconditionals If you live in Washington, D.C., then you live in the capital of the United States. If you live in the capital of the United States, then you live in Washington, D.C.

Homework: Pgs ; 6-32 evens Pgs ; 2-16 evens, all