2.2 Analyze Conditional Statements
Warm Up
Determine if each statement is true or false.
1. The measure of an obtuse angle is less than 90°.
2. All perfect-square numbers are positive.
3. Every prime number is odd.
4. Any three points are coplanar.
Objective: The learner will write definitions as conditional statements.
Vocabulary
Conditional Statement: _____________________________________________________________________________________________
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Definition
Symbol
Example 1
 If it is raining, then there are clouds in the sky.
 If the car is a Mustang, then it is a Ford.
Writing Conditional Statements
 All birds have feathers.
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 Two angles are supplementary if they are a linear pair.
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 All 90° angles are right angles.
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 When n = 9, n² = 81.
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 Tourists at the Alamo are in Texas.
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Negation: _______________________________________________________________________________________________
 The ball is red.
 Negation: _____________________________________________________________________________________
 The cat is not black.
 Negation: _____________________________________________________________________________________
Definition
Symbol
Converse: _______________________________________________________________________________________________
 If it is raining, then I will carry an umbrella.
 Converse: _______________________________________________________________________________________
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 If I am in Nutley, then I’m in New Jersey.
 Converse: _____________________________________________________________________________________
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Definition
Symbol
Inverse: _______________________________________________________________________________________________
 If it is a Corvette, then it is a Chevy.
 Inverse: _______________________________________________________________________________________
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 If you are a soccer player, then you are an athlete.
 Inverse: _______________________________________________________________________________________
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Definition
Symbol
Contrapositive: _______________________________________________________________________________________________
If A  99, then A is obtuse.
_____ Converse: _______________________________________________________________________________________________
_____ Inverse: _______________________________________________________________________________________________
_____ Contrapositive: _______________________________________________________________________________________________
Write the conditional, converse, inverse, and contrapositive for the conditional statement:
All whales are mammals
Conditional: __________________________________________________________________________________________________________
Converse: _____________________________________________________________________________________________________________
Inverse: _______________________________________________________________________________________________________________
Contrapositive: _______________________________________________________________________________________________________
Verifying Statements: ________________________________________________________________________________________________
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Use “Guitar players are musicians.” to write the following.
Conditional: __________________________________________________________________________________________________________
Converse: _____________________________________________________________________________________________________________
Inverse: _______________________________________________________________________________________________________________
Contrapositive: _______________________________________________________________________________________________________
Which statements are true? Give a counterexample if it is false.
Equivalent Statements: ____________________________________________________________________________________________
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Definition
Symbol
Biconditional: ________________________________________________________________________________________________________
 Example: ______________________________________________________________________________________________________
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If Mary is in theater class, she will be in the fall play. If Mary is in the fall play, she must be taking theater
class.
Biconditional: ________________________________________________________________________________________________________
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