Download 2.1 Conditional Statements

2.1 Conditional Statements
Mrs. Reser
Geometry
Fall 2008
Standards/Objectives:
Students will learn and apply geometric
concepts.
 Objectives:

Recognize and analyze a conditional
statement
 Write postulates about points, lines, and
planes using conditional statements.

Assignment:

Pp. 75-77 #4-28 all, 46-49 all.
Conditional Statement
A logical statement with 2 parts
 2 parts are called the hypothesis &
conclusion
 Can be written in “if-then” form; such as,
“If…, then…”

Conditional 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.
Counterexample
Used to show a conditional statement is
false.
 It must keep the hypothesis true, but
the conclusion false!
 It must keep the hypothesis true, but
the conclusion false!
 It must keep the hypothesis true, but
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.

Negation

Writing the opposite of a statement.
Ex: negate x=3
x≠3
 Ex: negate t>5
t 5

Converse

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.
Inverse

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.
Contrapositive

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.