CHAPTER 6:
INEQUALITIES IN GEOMETRY
6-2
INVERSES AND
CONTRAPOSITIVES
IF-THEN STATEMENTS
Recall that we have previously learned the
concept of if-then statements where a
hypothesis is followed by a conclusion.
We learned that the general form of an ifthen statement was structured like:
If p, then q.
INVERSE
An inverse is a conditional that is related to
an if-then statement:
Statement:
If p, then q.
Inverse:
If not p, then not q.
INVERSE
Example:
Statement:
If a person is mean, then they
are a fighter.
Inverse:
If a person is not mean, then
they are not a fighter.
CONTRAPOSITIVE
A contrapositive is a condition that is linked
to the inverse of a statement.
Inverse:
If not p, then not q.
Contrapositive:
If not q, then not p.
CONTRAPOSITIVE
Example:
Inverse: If a person is not mean, then they
are not a fighter.
Contrapositive:
If a person is not a
fighter, then they are not mean.
EXAMPLE
Write (a) the inverse and (b)
the contrapositive of the
conditional.
1. If a parallelogram is a
square, then it is a
rectangle.
a. If a parallelogram
is not a square,
then it is not a
rectangle.
b. If a parallelogram
is not a rectangle,
then it is not a
square.
EXAMPLE
Write (a) the inverse and (b)
the contrapositive for the
conditional.
a. If it is not snowing,
then the game is
not cancelled.
2. If it is snowing, then the
game is canceled.
b. If the game is not
cancelled, then it
is not snowing.
EXAMPLE
Write (a) the inverse and
a. If 2x + 1 ≤ 15, then x ≤
(b) the contrapositive for
7.
the conditional.
3. If 2x + 1 > 15, then x > 7
b. If x ≤ 7, then 2x + 1 ≤
15.
CLASSWORK/HOMEWORK
Classwork
• Pg. 210, Classroom Exercises 1-12
Homework
• Pgs. 210-212, Written Exercises 2-20
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