Download 2.1 Conditional Statements

2.1 Conditional Statements
Mrs. Blanco
Geometry Honors
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…”
• 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 2 angles are vertical, then they are congruent.
2. An object weighs one ton if it weighs 2000 lbs.
If an object weighs 2000 lbs, then it weighs one
ton.
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
• Switch the hypothesis & conclusion of a
conditional statement and negate each.
• 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.
Negation
• Writing the opposite of a statement.
• Ex: negate x=3
x≠3
• Ex: negate t>5
t 5
Example
• Conditional
– If
mÐB
• Inverse
• Converse
• Contrapositive
The original conditional
statement & its contrapositive
are logically equivalent.
The converse & inverse of a
conditional statement are
logically equivalent.
Counterexample
• Used to show a conditional statement is 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.
p. 75-78
#10, 12, 14,
15, 18, 19,
29-34,
40-43,
55, 56