Mrs Blanco Geometry Honors Conditional Statement A logical statement with 2 parts 2 parts are called the hypothesis amp conclusion Can be written in ifthen form such as If then ID: 529518
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Slide1
2.1 Conditional Statements
Mrs. Blanco
Geometry HonorsSlide2
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”Slide3
Ex: Underline the hypothesis & circle the conclusion.
If you are a brunette, then you have brown hair.
hypothesis conclusionSlide4
Ex: Rewrite the statement in “if-then” form
Vertical angles are congruent.
If
2 angles are vertical, then they are congruent
.
An object weighs one ton if it weighs 2000 lbs.
If an object weighs 2000 lbs, then it weighs one ton.Slide5
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.Slide6
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.Slide7
Contrapositive
S
witch
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.Slide8
Negation
Writing the opposite of a statement.
Ex
: negate x=3
x
≠3
Ex: negate t>5 t 5Slide9
Example
Conditional
If
Inverse
Converse
ContrapositiveSlide10
The original conditional statement & its
contrapositive
are logically equivalent.
The converse & inverse of a conditional statement
are logically equivalent.Slide11
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 x
2
=81, then x must equal 9.
counterexample: x could be -9
because (-9)
2
=81, but x
≠9.Slide12Slide13
p. 75-78
#10, 12, 14, 15,
18
, 19,
29-34,
40-43,
55, 56