Pre-AP Bellwork 7) The radius of a circle is 4 feet. Describe what happens to the circle’s area when the radius is doubled.

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

Chapter 5: Relationships Within Triangles 5.4 Inverses, Contrapositives, and Indirect Reasoning.

2.1 Conditional Statements

Problems to study for the chapter 2 exam

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

GEOMETRY Chapter 2 Notes.

Chapter 2 Conditional Statements Where You Will Have To Learn To Think Much More Formally In Other Words Logically.

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

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

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.

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

2.2 Conditional Statements Geometry Chapter 2: Reasoning and Proof.

Section 2-1: Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your.

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

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

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

Inductive Reasoning and Conditional Statements

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

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.

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)

Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your vegetables,

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

5-4 Inverses, Contrapositives, and Indirect Reasoning

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

Conditional Statements Chapter 2 Section 1. What is a conditional? A statement in “if-then” form ◦ If you do your work, then you can go out. ◦ If an animal.

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.

Section 2-1: Conditional Statements TPI 32C: Use inductive and deductive reasoning to make conjectures, draw conclusions,

1 2.1 Conditional Statements List the characteristics of conditional statements Write converses of conditional statements.

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

Holt Geometry 2-2 Conditional Statements 2-2 Conditional Statements Holt Geometry.

Conditional Statements (Cont.)

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.

Conditional Statements (Cont.). Using a Venn Diagram You can draw a Venn Diagram to illustrate conditional statements. – The set of things that satisfy.

2-1: Conditional Statements Chapter 2. Conditional Also referred to as an “if-then” statement: –“If you are not completely satisfied, then your money.

Conditional Statements Section 2-1. Objectives To recognize conditional statements. To recognize conditional statements. To write converses of conditional.

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.

If – Then Statements How can you use if-then statements in deductive reasoning? How is deductive reasoning different from inductive reasoning?

Conditional Statements Section 2-2. Objective Students will be able to recognize conditional statements and their parts to write converses, inverses,

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

Entry Task 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.

CONDITIONAL STATEMENTS Intro to AlgebraFarris 2015.

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.

Conditional Statements and Deductive Reasoning 2-1 – 2-3.

Conditional & Biconditional Statements Chapter 2 Section 2 1.

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

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

Conditional Statements.  Conditional Statement: A statement that can be written in the form “If p then q.”  Every Conditional Statement has 2 parts:

Objectives Students will…

Conditional Statements

Patterns and Inductive Reasoning

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

Conditional Statements

Lesson 2-3: Conditional Statements

Lesson 2.1 AIM: Conditional Statements

A logic statement written in if-then form.

SWBAT analyze statements in if-then form.

Conditional Statements

Conditional Statements

Conditional Statements

Logical Sequencing & Conditional Statements

Conditional Statements

2-2 Conditional Statements

Conditional Statements

Conditional Statements

2-2: Conditional Statements

Presentation transcript:

Pre-AP Bellwork 7) The radius of a circle is 4 feet. Describe what happens to the circle’s area when the radius is doubled.

Pre-AP Bellwork 8) Use the letters of the alphabet and create two different sequences that begin with the same two letters.

Pre-AP Bellwork 9) Draw a Venn Diagram to illustrate the following conditional statement. If the game is baseball, then the game is a team sport.

Pre-AP Bellwork 10) Write the sentence as a conditional statement: Two complementary angles form a right angle. Write the converse, inverse, and contrapositive of the conditional.

Reasoning and Proof Chapter 2

2-1 Conditional Statements What is a conditional statement? How do you write the converse of a conditional statement?

2-1Conditional Statements Conditional An if – then statement Two Parts: Hypothesis – The part following the if Conclusion – The part following the then

2-1 Conditional Statements

If today is the first day of fall, then the month is September. Hypothesis: Conclusion:

2-1 Conditional Statements If y – 3 = 5, then y = 8. Hypothesis: Conclusion:

2-1 Conditional Statements Many sentences can be written as conditionals. Can you identify the hypothesis and conclusion? Did you know a rectangle has four right angles? So, you are saying that if a figure is a rectangle, then it has four right angles?

2-1Conditional Statements A tiger is an animal. If something is a tiger, then it is an animal.

2-1 Conditional Statements Write each sentence as a conditional. An integer that ends with 0 is divisible by 5. A square has four congruent sides. If an integer ends with 0, then it is divisible by 5. If a figure is a square, then it has 4 congruent sides.

2-1 Conditional Statements Truth Value True or False A conditional is proven true if every time the hypothesis is true, the conclusion is also true. A conditional only needs 1 counterexample to be proven false.

2-1 Conditional Statements Show the conditional is false by finding a counterexample: If it is February, then there are only 28 days in the month. Since 2008 was a leap year, February had 29 days.

2-1 Conditional Statements Show the conditional is false by finding a counterexample: If the name of a state contains the word New, then the state borders an ocean. New Mexico is a state, but it does not border an ocean.

2-1 Conditional Statement A Venn diagram can be used to better understand true conditional statements. If you live in Chicago, then you live in Illinois. Chicago Illinois

2-1 Conditional Statements Draw a Venn diagram to illustrate this conditional: If something is a cocker spaniel, then it is a dog. Dog Cocker Spaniel

2-1 Conditional Statements Converse Switches the hypothesis and conclusion of a 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 Conditional Statements Write the converse of the following conditional. Conditional If two lines are not parallel and do not intersect, then they are skew. Converse If two lines are skew, then they are not parallel and do not intersect.

2-1 Conditional Statements In the last two examples, both the conditional and its converse are true. This is not always the case. Conditional: If a figure is a square, then it has 4 sides. Converse: If a figure has 4 sides, then it is a square. This is not true, as any rectangle can be used as a counterexample.

2-1 Conditional Statements Write the converse of each conditional statement. Determine the truth value of the conditional and its converse. If two lines do not intersect, then they are parallel. If two lines are parallel, then they do not intersect. The conditional is false, but the converse is true. If x = 2, then |x| = 2. If |x| = 2, then x = 2. The conditional is true, but the converse is false.

2-1 Conditional Statements Conditional Statements and Converses StatementExampleSymbolic Form You Read It Conditional If an angle is a straight angle, then its measure is 180. p → qIf p, then q. Converse If the measure of an angle is 180, then it is a straight angle. q → pIf q, then p.

2-1 Conditional Statements Homework Pages 72 – – 39; 42; 43; 47

5-4 Inverses, Contrapositives, and Indirect Reasoning Negation Opposite truth value “Knoxville is the capital of Tennessee.” False Negation: “Knoxville is not the capital of Tennessee.” True

5-4 Inverses, Contrapositives, and Indirect Reasoning Write the negation for each statement. Angle ABC is obtuse. Angle ABC is not obtuse. Lines m and n are not perpendicular. Lines m and n are perpendicular.

5-4 Inverses, Contrapositives, and Indirect Reasoning Inverse Negates the hypothesis and conclusion of a conditional statement. Conditional If a figure is a square, then it is a rectangle. Inverse If a figure is not a square, then it is not a rectangle

5-4 Inverses, Contrapositives, and Indirect Reasoning Contrapositive Switches the hypothesis and conclusion

5-4 Inverses, Contrapositives, and Indirect Reasoning Conditional If a figure is a square, then it is a rectangle. Inverse If a figure is not a square, then it is not a rectangle. Contrapositive If a figure is not a rectangle, then it is not a square.

Conditional Statements and Converses StatementExampleSymbolic Form You Read It Conditional If an angle is a straight angle, then its measure is 180. p → qIf p, then q. Converse If the measure of an angle is 180, then it is a straight angle. q → pIf q, then p. Negation An angle is not a straight angle. ~pNot p. Inverse If an angle is not a straight angle, then its measure is not 180. ~p → ~qIf not p, then not q. Contrapositive If an angle’s measure is not 180, then it is not a straight angle. ~q → ~pIf not q, then not p..