9/12/2011
Section 2 – 1
Conditional StatementS
Brainstorming Ideas…
Learning Targets
1. Taking statements and writing them as
mathematically logical statements.
2. Writing the converse, inverse and contrapositive
of each statement and be able to determine if it
is TRUE or FALSE.
Definitions
• Conditional Statements
• IF – THEN STATEMENTS
• Used to clarify statements that COULD be
confusing.
• An angle that is acute is 30 degrees.
• Two Parts
• The IF (Hypothesis)
• The THEN (Conclusion)
• If you don’t do your homework then…
An acute angle has measure of 30
degrees…
• This is a true statement – but can be true for
MANY different angle measures.
• CONDITIONAL STATEMENT
• Needs an IF
• If an angle measures 30 degrees
• Followed by a THEN
• Then it is acute.
• If an angle measures 30 degrees then it is acute.
Example
• Identify the HYPOTHESIS and CONCLUSION
of the following conditional statement.
IF TWO LINES ARE PARALLEL THEN THEY ARE COPLANAR.
TRUTH VALUE
• Conditional statements can be true or false
• If you drink Gatorade, then you will be like Mike
• If a conditional is FALSE, you must provide a
counterexample that SHOWS why it is false.
• You could be like Tiger Woods
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9/12/2011
Take the following statement
and write it as a TRUE
conditional.
A triangle has three sides
INVERSE of a Conditional
Statement
• The negation of both the hypothesis and
conclusion of the statement.
If a figure is a triangle, then it has three sides.
INVERSE: If a figure is NOT a triangle, then it does
NOT have three sides.
TRUE
CONVERSE of a Conditional
Statement
• Taking the hypothesis and conclusion and
switching them.
IF A FIGURE IS A TRIANGLE, THEN IT HAS THREE
SIDES.
Converse:
IF A FIGURE HAS THREE SIDES, THEN IT IS A
TRIANGLE.
TRUE
FALSE
TRY ONE!
• Write a true conditional statement. State the
INVERSE, CONVERSE and CONTRAPOSITIVE of
the true conditional. Be sure to state its truth
value – give a counter example when needed.
AN ANGLE THAT MEASURES 120 DEGREES IS
OBTUSE.
or
FALSE
CONTRAPOSITVE of a Conditional
Statement
• Taking the CONVERSE of a statement and
negating it.
IF A FIGURE IS A TRIANGLE, THEN IT HAS THREE
SIDES.
Converse:
IF A FIGURE HAS THREE SIDES, THEN IT IS A
TRIANGLE.
Contrapositive:
IF A FIGURE DOES NOT HAVE THREE SIDES, THEN IT
IS NOT A TRIANGLE.
AN ANGLE THAT MEASURES 120
DEGREES IS OBTUSE.
If an angle measures 120 degrees then it is obtuse.
TRUE
Inverse:
If an angle does not measure 120 degrees then it is not
obtuse.
FALSE – 134 degrees
Converse:
If an angle is obtuse, then it measures 120 degrees.
FALSE – 134 degrees
Contrapositive
If an angle is not obtuse, then it does not measure 120
degrees.
TRUE
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