2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

Slides:

Advertisements

Similar presentations

Inverses, Contrapositives, and Indirect Reasoning

Advertisements

Inverses, Contrapositives, and Indirect Reasoning

Geometry 2.2 Big Idea: Analyze Conditional Statements

Conditional Statements

Write the negation of “ABCD is not a convex polygon.”

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

Check your skills 2. Homework Check Notes 4. Practice 5. Homework/work on Projects.

Section 2.1 Notes Conditional Statements. Conditional Statement A type of logic statement that has two parts: a hypothesis and a conclusion We will write.

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

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

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.

Do Now Each of the letters stands for a different digit. The first digit in a number is never zero. Replace the letters so that each sum is correct.

Inductive/Dedu ctive Reasoning Using reasoning in math and science.

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)

2.2 Definitions and Biconditional Statements. Definition Two lines are called perpendicular lines if they intersect to form a right angle. A line perpendicular.

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

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

 What are conditionals & biconditionals?  How do you write converses, inverses, and contrapositives?

Conditional Statement A conditional statement has two parts, a hypothesis and a conclusion. When conditional statements are written in if-then form, the.

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.

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)

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

Section 2-2: Conditional Statements. Conditional A statement that can be written in If-then form symbol: If p —>, then q.

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.

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.

Unit 2-2: Conditional Statements Mr. Schaab’s Geometry Class Our Lady of Providence Jr.-Sr. High School

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?

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.

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.

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

Inductive Reasoning Notes 2.1 through 2.4. Definitions Conjecture – An unproven statement based on your observations EXAMPLE: The sum of 2 numbers is.

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.

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

Conditional Statements

Analyze Conditional Statements

Section 2.1 Conditional Statements

Conditional Statements

Conditional Statements

Opener 5. If a number greater than 2 is even, then it’s not prime

Chapter 2 Quiz Review.

A logic statement written in if-then form.

2-2 Conditional Statements

2-2 Conditional Statements

If-Then Statements/Converses

2.1 Conditional Statements

2.2 Analyze Conditional Statements

Conditional Statements

2.1-2 Inductive Reasoning and Conditional Statements

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

Conditional Statements

Chapter 2.2 Notes: Analyze Conditional Statements

Section 2.2 Definitions and Biconditional Statement

G7 Conditional Statements

More Conditional Statements

2.2 If - Then Statements OBJ: (1)To Write Statements in If-Then Form

Logic and Reasoning.

2.1 Continued: Definitions and Biconditionals

Conditional Statements

Different Forms of Conditional Statements

Presentation transcript:

2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive Reasoning and Proofs 2.1 conditionals, 2.2 Biconditionals, 5.4 inverse and contrapositive

Agenda Warm-up Homework check 2.1 conditionals, 2.2 biconditionals, 5.4 inverse and contrapositive Practice Homework

Warm-Up: 1. 2. 3.

3-d Coordinate Plane! Find the coordinates for: O (0,0,0) N (0, -4, 0) K (-3, 0, 0) J (0,0, 4) M (0, -4, 4) H (-3, -4, 4) L (-3, 0, 4) I (-3, -4, 0)

Homework Check

2-1, 5-4, 2-2 Reasoning and Proof Negate – to add or remove the word “Not” Ex. Negate: “<A is a right <.” Becomes: <A is not a right <. Ex. Negate: “I am not cold.” Becomes: I am cold.

Conditional Statement: an if-then statement. (p  q) All conditional statements have 2 parts. A hypothesis A conclusion.

Hypothesis: (p) Follows “IF” Conclusion: (q) Follows “THEN” Ex: If today is Valentines Day, then the month is February. **When stating these do NOT include the words “if” or “then” Hypothesis: Today is Valentines Day. Conclusion: The month is February.

EX: Three points are collinear, if they are all in a line EX: Three points are collinear, if they are all in a line. Hypothesis: Three points are all in a line. Conclusion: The three points are collinear.

Converse: SWITCHES the hypothesis and the conclusion EX: Conditional: If two lines intersect to form right angles, then they are perpendicular Write the converse: If two lines are perpendicular then the two lines intersect to form right angles.

Inverse: NEGATE the hypothesis and the conclusion **If not p, then not q.** EX: Conditional: If two lines intersect to form right angles, then they are perpendicular Write the Inverse: If two lines do not intersect to form right angles, then they are not perpendicular.

Contrapositive: SWITCH AND NEGATE Conditional: If p, then q Contrapositive: SWITCH AND NEGATE Conditional: If p, then q. Contrapositive: *If not q, then not p.* -Logically equivalent to the original conditional -If conditional is true, then the contrapositive is true.

EX: Conditional: If two lines intersect to form right angles, then they are perpendicular Contrapositive: If two lines are not perpendicular then they do not intersect to form right angles.

Biconditional: p if and only if q (p iff Biconditional: p if and only if q (p iff. q)  occurs when a statement and its converse are true.

Counterexample: an example that shows the hypothesis can be true while the conclusion is false, thereby proving the statement is false. Ex. Conditional: If two angles are adjacent then they are a linear pair. Counterexample: <ABC and <CBD are Adjacent but not a linear Pair.

Examples Ex1. An angle that measures 90 ̊ is a right <. Write As a conditional: If an angle measures 90 ̊, then it is a right <. Write the Converse: If an angle is a right <, then it measures 90 ̊

Ex1. An angle that measures 90 ̊ is a right < Ex1. An angle that measures 90 ̊ is a right <. Write the Inverse: If an angle does not measure 90 ̊, then it is not a right <. Write the Contrapositive: If an angle is not a right <, then it does not measure 90 ̊

Ex. If possible, write the biconditional of each statement Ex. If possible, write the biconditional of each statement. If not explain. 2. If an angle is a straight angle, then it measures 180 ̊ Converse: If an angle measures 180 ̊, then it is a straight angle. (True) Biconditional: An angle is a straight < if and only if it measures 180 ̊.

3. If 2 angles are a linear pair, then their sum is 180 ̊ 3. If 2 angles are a linear pair, then their sum is 180 ̊. Converse: If 2 angles’ sum is 180, then they are a linear pair. –False Counterexample: No biconditional because the converse is false!

Most good definitions can be written as biconditionals Most good definitions can be written as biconditionals. **You can determine a definition is not good by finding a counterexample.

Homework Worksheet Scrapbook Project due Friday Distance/Midpoint Mini-Project due Sept 18