Chapter 2 Reasoning Proof 2 1 Conditional Statements

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Chapter 2 Reasoning & Proof

Chapter 2 Reasoning & Proof

2 – 1 Conditional Statements Objectives: To recognize conditional statements To write converses of

2 – 1 Conditional Statements Objectives: To recognize conditional statements To write converses of conditional statements

“If you are not completely satisfied, then your money will be refunded. ” Conditional:

“If you are not completely satisfied, then your money will be refunded. ” Conditional: an if-then statement Hypothesis: the part of the conditional that follows “if” Conclusion: the part of the conditional that follows “then”

Example 1 Identifying the Hypothesis & Conclusion Identify the hypothesis and the conclusion of

Example 1 Identifying the Hypothesis & Conclusion Identify the hypothesis and the conclusion of each conditional statement. A. If today is the first day of fall, then the month is September. B. If y – 3 = 5, then y = 8.

Example 2 Writing a Conditional Write each sentence as a conditional. A. A rectangle

Example 2 Writing a Conditional Write each sentence as a conditional. A. A rectangle has four right angles. B. A tiger is an animal

C. An integer that ends with 0 is divisible by 5 D. A square

C. An integer that ends with 0 is divisible by 5 D. A square has four congruent sides

Truth Value: either TRUE or FALSE TRUE: TRUE every time the hypothesis is true,

Truth Value: either TRUE or FALSE TRUE: TRUE every time the hypothesis is true, the conclusion is also true. FALSE: FALSE find ONE counterexample for which the hypothesis is true and the conclusion is false.

Example 3 Finding a Counterexample Show that this conditional is false by finding a

Example 3 Finding a Counterexample Show that this conditional is false by finding a counterexample: A) If it is February, then there are only 28 days in the month.

Show that this conditional is false by finding a counterexample. B) If the name

Show that this conditional is false by finding a counterexample. B) If the name of a state contains the word New, then the state borders an ocean.

Example 4 Using a Venn Diagram A) Draw a Venn diagram to illustrate this

Example 4 Using a Venn Diagram A) Draw a Venn diagram to illustrate this conditional. If you live in Little Falls, then you live in New Jersey.

B) Draw a Venn diagram to illustrate this conditional If something is a whole

B) Draw a Venn diagram to illustrate this conditional If something is a whole number, then it is an integer.

Homework : Page 71 – 72; 2 – 22 Even

Homework : Page 71 – 72; 2 – 22 Even

2 – 1 Continued Objective: To write converses of conditional statements

2 – 1 Continued Objective: To write converses of conditional statements

Converse: Switches the hypothesis and conclusion of a conditional Conditional: If an angle has

Converse: Switches the hypothesis and conclusion of a conditional Conditional: If an angle has measure 40, then it is acute. Converse: If an angle is acute, then it has measure 40.

Example 5 Writing the Converse of a Conditional Write the converse of the following

Example 5 Writing the Converse of a Conditional Write the converse of the following conditional. A) 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.

B) Write the converse of the following conditional. If two lines are not parallel

B) Write the converse of the following 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.

Example 6 Finding the Truth Value of a Converse Consider this true conditional statement.

Example 6 Finding the Truth Value of a Converse Consider this true conditional statement. Write the converse and determine its truth value. A) If a figure is a square, then it has four sides. Converse: If a figure has four sides, then it is a square. Truth Value of Converse: FALSE

Example 7 Real-World Connection “Why you might just as well say that ‘I see

Example 7 Real-World Connection “Why you might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see’!” – Mad Hatter

“Why you might just as well say that ‘I see what I eat’ is

“Why you might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see’!” – Mad Hatter A) Explain why the Mad Hatter is wrong.

“…’I breathe when I sleep’ is the same thing as ‘I sleep when I

“…’I breathe when I sleep’ is the same thing as ‘I sleep when I breathe’!” – Dormouse B) Explain why the Dormouse is wrong.

Ticket Out Use “If a circle’s radius is 2 m, then its diameter is

Ticket Out Use “If a circle’s radius is 2 m, then its diameter is 4 m” to answer # 1 – 3. 1) Identify the hypothesis & conclusion 2) Write the converse Determine the truth value of the conditional and its converse (include counterexamples if necessary) 4) True or False? If lines do not intersect, then they are parallel. 5) True or False? All numbers containing the digit 0 are divisible by 10. 3)

Homework Textbook Page 37; # 23 – 35 All

Homework Textbook Page 37; # 23 – 35 All

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