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 if-then 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.

2. If it is snowing, then the game is canceled.

a. If it is not snowing, then the game is not cancelled.

b. If the game is not cancelled, then it is not snowing.

EXAMPLE

Write (a) the inverse and (b) the contrapositive for the conditional.

3. If 2x + 1 > 15, then x > 7

a. 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 even