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Lesson 5-4
Inverses, Contrapositives, and Indirect Reasoning
Write the negation of a statement and the inverse and contrapositive of a conditional
statement.
Use indirect reasoning.
Vocabulary
Definition
Symbols
A conditional statement is a statement that can be written in the form
The converse is the statement formed by
The negation of statement p is
The inverse is the statement formed by
The contrapositive is the statement formed by
logically equivalent statements______________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
indirect reasoning ________________________________________________________________
________________________________________________________________________________
indirect proof (proof by contradiction)
Step 1
Step 2
Step 3
Pearson Prentice Hall Geometry
Lesson 5-4
Page 1 of 2
Examples
Writing the Negation of a Statement
Write the negation of “ABCD is not a convex polygon.”
Writing the Inverse and Contrapositive
Write the inverse and contrapositive of the conditional statement “If ∆ABC is equilateral, then it is
isosceles.”
The First Step of an Indirect Proof
Write the first step of an indirect proof.
Prove: A triangle cannot contain two right angles.
Identify Contradictions
Identify the two statements that contradict each other.
I. P, Q, and R are coplanar.
II. P, Q, and R are collinear.
III. m∠PQR = 60
Two statements contradict each other when they cannot both be true at the same time.
Examine each pair of statements to see whether they contradict each other.
Indirect Proof
Write an indirect proof.
Prove: ∆ABC cannot contain 2 obtuse angles.
HW (Day 1): pp. 283-286 #7, 8, 11, 13, 15-19, 21-23, 25, 26-36even
HW (Day 2): pp. 284-286 #27, 28, 35, 37, 38, 41
Review for 5-3 Quiz – pg. 279 #9, 10 pp. 297-298 #1-4, 8-22
Pearson Prentice Hall Geometry
Lesson 5-4
Page 2 of 2
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