Lesson 2.2 Analyze Conditional
Statements
Goal: The learner will write definitions as
conditional statements.
Vocabulary

Conditional Statement: a logical
statement that has a hypothesis
and a conclusion.
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If-then form: format for a conditional
statement.
Hypothesis: the “if” part
Conclusion: the “then” part
Hypothesis must always be true.
Example

If it is raining, then there are clouds in the sky.
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If the car is a Mustang, then it is a Ford.
Writing Conditional Statements


All birds have feathers.
Two angles are supplementary if
they are a linear pair.
More Examples
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All 90° angles are right angles.
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When n = 9, n² = 81.

Tourists at the Alamo are in Texas.
Negation: the opposite of the
original statement.

The ball is red.
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Negation:
The cat is not black.
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Negation:
Converse: flip-flop the hypothesis and
conclusion.
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If it is raining, then I will carry an umbrella.
 Converse
If I am in Roadtown, then I’m in Tortola.
 Converse
Inverse: Negate both the
hypothesis and conclusion

If it is a Corvette, then it is a Chevy.
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Inverse:
If you are a soccer player, then you are an
athlete.
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Inverse:
Contrapositive: negate and flip-flop the
hypothesis and conclusion.
If A  99, thenA is obtuse.
Converse:
Inverse:
Contrapositive:
Are these statements true?
Write the if-then, converse, inverse, and
contrapositive for the conditional statement: All
whales are mammals
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If-then: If it is a whale, then it is a
mammal.
Converse: If it is a mammal, then it
is a whale.
Inverse: If it is not a whale, then it
is not a mammal.
Contrapositive: If it is not a
mammal, then it is not a whale.
Verifying Statements
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You must show the conclusion is
true every time the hypothesis is
true.
It only takes one counterexample to
show it’s false.
Use “Guitar players are musicians.” to write the
following.
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“If-then”
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Converse
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Inverse
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Contrapositive
Which statements are true? Give a counterexample if
it is false.
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If a polygon is equilateral, then the
polygon is regular.
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Converse

Inverse
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Contrapositive
Equivalent Statements: when two
statements are both true or false.
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Conditional Statement and its
contrapositive are either both true
or false.
Converse and inverse are either
both true or false.
Definitions as Conditional Statments
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Any definition can be written as “ifthen” or as its converse.
Example:
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Right Angles: If the angle measure is
90◦, then it is a right angle.
Biconditional Statement: When a “If-Then” and its
converse are true you can write them as a single
statement.
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All definitions are biconditional.
Example:
 Perpendicular lines: If the angle
measure is 90◦, then then it is a right
angle.
 Converse: If the angle is a right angle,
then the its measure is 90◦.
 Biconditional: An angle is a right angle if
and only if the its measure is 90◦
Example

Write the definition of straight angle
as a biconditional statement.
Another 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.