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Learning Targets
 I can recognize conditional statements and their parts.
 I can write the converse of conditional statements.
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Geometry
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Conditional Statement
 A conditional statement has two parts, a hypothesis
and a conclusion.
 When conditional statements are written in if-then
form, the part after the “if” is the hypothesis, and the
part after the “then” is the conclusion.
 p→q
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Example 1: State the hypothesis and conclusion.
 If you are 13 years old, then you are a teenager.
 Hypothesis:
 You are 13 years old
 Conclusion:
 You are a teenager
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Example 1: Rewrite in the if-then form
 All mammals breathe oxygen
 If an animal is a mammal, then it breathes oxygen.
 A number divisible by 9 is also divisible by 3
 If a number s divisible by 9, then it is divisible by 3.
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Negation
 The negative of the statement
 Example: Write the negative of the statement
 A is acute
 A is not acute
 ~p represents “not p” or the negation of p
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Converse, Inverse and Contrapositive
 Converse
 The converse of a conditional is formed by switching the
hypothesis and the conclusion.
 The converse of p → q is q → p
 Inverse
 Negate the hypothesis and the conclusion
 The inverse of p → q, is ~p → ~q
 Contrapositive
 Negate the hypothesis and the conclusion of the converse
 The contrapositive of p → q, is
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Geometry
~q → ~p.
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Example
 Write the (a) inverse, (b) converse, and (c)
contrapositive of the statement.
 If two angles are vertical, then the angles are congruent.
 (a) Inverse: If 2 angles are not vertical, then they are
not congruent.
 (b) Converse: If 2 angles are congruent, then they are
vertical.
 (c) Contrapositive: If 2 angles are not congruent, then
they are not vertical.
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Equivalent Statements
 When 2 statements are both true or both false
 A conditional statement is equivalent to its contrapositive.
 The inverse and the converse of any conditional are equivalent.
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Geometry
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Conditional Statement
Converse
Inverse
Contrapositive
Geometry
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