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Section 2-1: Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your vegetables, then you will grow up to be big and strong. conditional statement: ___________ _________________________ _____ an if- then stateme nt hypothesis: ____________________ conclusion: ____________________ follows the if part follows the then part

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

Section 2-1: Conditional StatementsGoal: Be able to recognize conditional statements, and

to write converses of conditional statements.

If you eat your vegetables, then you will grow up to be big and strong.

conditional statement: _________________________________________

an if-thenstatement

hypothesis: ____________________

conclusion: ____________________

follows the if part

follows the then part

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

If you eat your vegetables, then you will grow up to be big and strong.

Hypothesis: ______________________You eat your vegetables

Conclusion: ______________________________________________________

You will grow up to be bigand strong

If 2 lines are perpendicular, then they form a right angle.Hypothesis: ______________________

Conclusion: ______________________2 lines are perpendicularThey form a right angle

Page 3: Section 2-1: Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your

Writing Conditional Statements

Ex 1: An angle of 150° is obtuse._____________________________________If an angle is 150°, then it is obtuse.

Ex 2: A parallelogram has opposite sides parallel.

If a figure is a parallelogram, then it has __________________________________________________________________________opposite sides parallel.

Page 4: Section 2-1: Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your

A conditional can have a _____________ of true or false.

truth value

Find a counterexample where the hypothesis is _________ and the conclusion is _________.

truefalse

Ex 3: Odd integers less than 10 are prime.

Counterexample: _____________________9Ex 4: If I scored a goal, then I played soccer.Counterexample: _____________________hockey

(If an odd integer is less than 10, then it is prime.)

Page 5: Section 2-1: Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your

Use a Venn Diagram to illustrate the conditional statement.

Ex 4: If a food is a tomato, then it is a fruit.

tomato

fruit

Page 6: Section 2-1: Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your

converse: ________________________________________________________________

switches the hypothesis and conclusion of a conditional statement

Conditional: If two lines have the same slope, then the lines are parallel.Converse: _______________________________________________________________

Ex 5: Conditional: If 3 points are noncollinear, then they determine a plane.Converse: _______________________________________________________________

If 3 points determine a plane, then they are noncollinear.

If two lines are parallel, then they have the same slope.

Page 7: Section 2-1: Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your

inverse: ____________________________________________________________________________________________________

negates the hypothesis and negates the conclusion of a conditional statement contrapositive:____________________________________________________________

switches the hypothesis and conclusion and negates both of them Conditional: If two lines have the same slope, then the lines are parallel.inverse: _______________________________________________________________

If two lines do not have the same slope, then the lines are not parallel.

contrapositive: __________________________________________________________

If two lines are not parallel, then they do not have the same slope.

Page 8: Section 2-1: Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your

Finding the Truth Value of a Conditional and ConverseEx 6: Conditional: If 2 lines do not intersect, then they are parallel.

Converse: _______________________________________________________________

If 2 lines are parallel, then they do not intersect.

Conditional is : _______________________Converse is : _________________________

False (counterexample: skew) True

Page 9: Section 2-1: Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your

Ex 7: Conditional: If a figure is a square, then it has four right angles.

Converse: _______________________________________________________________

If a figure has four right angles, then it is a square.

Conditional is : _______________________

Converse is : _________________________

True

False (counterexample: rectangle)

Page 10: Section 2-1: Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your

SummaryIf a circle’s radius is 3 m, then its circumference is 6π m.

1.) Identify the hypothesis and conclusion.Hypothesis: ____________________________________Conclusion: ____________________________________

2.) Write the converse.____________________________________________________________________________________________

3.) Determine the truth value of the conditional and its converse.Conditional:____________________________________Converse: _____________________________________

A circle’s radius is 3 m Its circumference is 6 π m

If a circle’s circumference is 6 π m, then its radius is 3 m.

TrueTrue

Page 11: Section 2-1: Conditional Statements Goal: Be able to recognize conditional statements, and to write converses of conditional statements. If you eat your

4.) Show that the conditional is false by finding a counterexample.All numbers containing the digit 0 are divisible by 10.

(If a number contains the digit 0, then it is divisible by 10.)

Counterexample: _______________________________105


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