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2-4 Conditionals, Converses & Biconditionals LEARNING GOALS – LESSON 2.2 TO 2.4 2.4.1: Recognize, understand, and write conditional statements. 2.4.2: Analyze conditional statements to see if they are true or not. If they are false, be able to provide counter examples to support of your claim. 2.4.3: Be able to write the converse of a conditional statement. 2.4.4. Be able to write a biconditional from a conditional statement, & evaluate the biconditional. Ex 1A: Identify the Parts of a Conditional Statement Write a conditional statement from each of the following. a. If a butterfly has a curved black line on its hind wing, then it is a viceroy. Hypothesis: _______________________________________________ Conclusion: _______________________________________________ b. A number is an integer if it is a natural number. Hypothesis: _______________________________________________ Conclusion: _______________________________________________ 2-4 Conditionals, Converses & Biconditionals Ex. 1B: Writing a Conditional Statement Write a conditional statement from each of the following. a. The Midpoint of M of a segment bisects the segment. __________________________________________________________________ b. Two angles that are complementary are acute. __________________________________________________________________ Ex. 2: Determining Truth & Counterexamples Write a conditional statement from each of the following. a. If an angle is acute, then its measure is 35°. __________________________________________________________________ b. If an angle is obtuse, then it’s measure is greater than 90° but less than 180°. __________________________________________________________________ 2-4 Conditionals, Converses & Biconditionals Ex. 3A: Writing Converses & Determining Truth Value Ex. 3B: Writing Converses & Determining Truth Value For each conditional statement, write the converse & determine the truth value. a. If a ray is a bisector of an angle, then it divides an angle into two congruent angles. _________________________________________________________________ b. If y = 4, then y2 = 16. __________________________________________________________________ 2-4 Conditionals, Converses & Biconditionals Ex. 4A: Writing Biconditionals & Determining Truth Value Write the conditional and converse within each biconditional. a. A solution is a base if and only if its pH greater than 7. ________________________________________________________________ __________________________________________________________________ b. A polygon is a quadrilateral if and only if it has four sides. ______________________________________________________________ _______________________________________________________________ Ex. 4B: Writing Biconditionals & Determining Truth Value Write the definition as a biconditional. An isosceles triangle has at least 2 congruent sides. ________________________________________________________________ __________________________________________________________________ NOTE: A biconditional statement is false if either the conditional statement is false, or its converse is false. Ex. 4B: Writing Biconditionals & Determining Truth Value Determine if each biconditional is true. If flase, give a counterexample a = 3 and b = 4 if and only if ab = 12. ________________________________________________________________