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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:
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Conclusion:
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b. A number is an integer if it is a natural number.
Hypothesis:
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Conclusion:
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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.
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b. Two angles that are complementary are acute.
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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°.
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b. If an angle is obtuse, then it’s measure is greater than 90° but
less than 180°.
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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.
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b. If y = 4, then y2 = 16.
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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.
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b. A polygon is a quadrilateral if and only if it has four sides.
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Ex. 4B: Writing Biconditionals & Determining Truth Value
Write the definition as a biconditional.
An isosceles triangle has at least 2 congruent sides.
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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.
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