2.1 Conditional Statements2.1 Conditional Statements

Mrs. StelterGeometryFall 2010

Standards/Objectives:

Students will learn and apply geometric concepts.

Objectives:Recognize and analyze a conditional

statementWrite postulates about points, lines, and

planes using conditional statements.

Conditional StatementConditional Statement

A logical statement with 2 parts2 parts are called the hypothesis &

conclusionCan be written in “if-then” form; such as,

“If…, then…”

Conditional StatementConditional Statement

Hypothesis is the part after the word “If”Conclusion is the part after the word

“then”

Ex: Underline the hypothesis & circle the conclusion.

If you are a brunette, then you have brown hair.

hypothesis conclusion

Ex: Rewrite the statement in “if-then” form

1. Vertical angles are congruent.

If there are 2 vertical angles, then they are congruent.

If 2 angles are vertical, then they are congruent.

Ex: Rewrite the statement in “if-then” form

2. An object weighs one ton if it weighs 2000 lbs.

If an object weighs 2000 lbs, then it weighs one ton.

CounterexampleCounterexample

Used to show a conditional statement is false.

It must keep the hypothesis true, but It must keep the hypothesis true, but the conclusion false!the conclusion false!

It must keep the hypothesis true, but It must keep the hypothesis true, but the conclusion false!the conclusion false!

It must keep the hypothesis true, but It must keep the hypothesis true, but the conclusion false!the conclusion false!

Ex: Find a counterexample to prove the statement is false.

If x2=81, then x must equal 9.

counterexample: x could be -9

because (-9)2=81, but x≠9.

Venn Diagrams

Dogs

labs

If it is a lab, then it is a dog

Michigan

Detroit

If you live in Detroit, then you live in Michigan

NegationNegation

Writing the opposite of a statement.

Ex: negate x=3

x≠3Ex: negate t>5

t 5

ConverseConverse

Switch the hypothesis & conclusion parts of a conditional statement.

Ex: Write the converse of “If you are a brunette, then you have brown hair.”

If you have brown hair, then you are a brunette.

InverseInverse

Negate the hypothesis & conclusion of a conditional statement.

Ex: Write the inverse of “If you are a brunette, then you have brown hair.”

If you are not a brunette, then you do not have brown hair.

ContrapositiveContrapositive

Negate, then switch the hypothesis & conclusion of a conditional statement.

Ex: Write the contrapositive of “If you are a brunette, then you have brown hair.”

If you do not have brown hair, then you are not a brunette.

The original conditional statement & its contrapositive will always have the same meaning.

The converse & inverse of a conditional statement will always have the same meaning.

Assignment:

Pp. 83 (2-34)Pp. 85 (54-58)