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

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Conditional Statements

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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 statement hypothesis: ____________________ conclusion: ____________________ follows the if part follows the then part

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 big and strong If 2 lines are perpendicular, then they form a right angle. Hypothesis: ______________________ Conclusion : ______________________ 2 lines are perpendicular They form a right angle

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.

A conditional can have a _____________ of true or false. truth value Find a counterexample where the hypothesis is _________ and the conclusion is _________. true false Ex 3: Odd integers less than 10 are prime. Counterexample: _____________________ 9 Ex 4: If I scored a goal, then I played soccer. Counterexample: _____________________ hockey (If an odd integer is less than 10, then it is prime.)

Use a Venn Diagram to illustrate the conditional statement. Ex 4: If a food is a tomato, then it is a fruit. tomato fruit

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.

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.

Finding the Truth Value of a Conditional and Converse Ex 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

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)

Summary If 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. True

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