Transcript If-Then Statements

If-Then Statements
Geometry
Chapter 02
A BowerPoint Presentation
Conditional
• If a  then b
• Hypothesis is a
• Conclusion is b
Conditional
• If a  then b
• If Skittles®, then there’s an
‘S’ on it
• What is the hypothesis?
Conditional
• If a  then b
• If Skittles®, then there’s an
‘S’ on it
• What is the hypothesis?
–If Skittles
Conditional
• If a  then b
• If Skittles®, then there’s an
‘S’ on it
• What is the conclusion?
Conditional
• If a  then b
• If Skittles®, then there’s an
‘S’ on it
• What is the conclusion?
–(Then) there’s an ‘S’ on it
Conditional
• If a  then b
• If Skittles®, then there’s an
‘S’ on it
• Is this true?
Conditional
• If a  then b
• If Skittles®, then there’s an
‘S’ on it
• True!
Converse
• If b  then a
Converse
• If b  then a
• If there’s an ‘S’ on it, then
Skittles®
Converse
• If b  then a
• If there’s an ‘S’ on it, then
Skittles®
• Is this true?
Converse
• If b  then a
• If there’s an ‘S’ on it, then
Skittles®
• False!
Biconditional
• If the conditional and the converse are
BOTH true, we can write a biconditional
statement.
• If measure of Angle B is 90°,then Angle B
is a right angle. (True)
• If Angle B is a right angle, then measure of
Angle B is 90°. (True)
• So…
Biconditional
• If measure of Angle B is 90°,then Angle B is a
right angle.
• If Angle B is a right angle, then measure of Angle
B is 90°.
• Combined into a biconditional statement:
• The measure of Angle B is 90° if and
only if Angle B is a right angle.
Biconditional
• You try making a biconditional statement
from this true conditional and its converse:
• If today is February 14, then today is
Valentine’s Day.
• If today is Valentine’s Day, then today is
February 14.
(Remember to use IF AND ONLY IF)
Biconditional
• Today is February 14 if and only if today is
Valentine’s Day
or
• Today is Valentine’s Day if and only if
today is February 14.
• Biconditionals look like a b
Contrapositive
• If not b  then not a
Contrapositive
• If not b  then not a
• If there’s not an ‘S’ on it,
then not Skittles®
Contrapositive
• If not b  then not a
• If there’s not an ‘S’ on it,
then not Skittles®
• Is this true?
Contrapositive
• If not b  then not a
• If there’s not an ‘S’ on it,
then not Skittles®
• True!
Inverse
• If not a  then not b
Inverse
• If not a  then not b
• If not Skittles®, then it
doesn’t have an ‘S’ on it
Inverse
• If not a  then not b
• If not Skittles®, then it
doesn’t have an ‘S’ on it
• Is this true?
Inverse
• If not a  then not b
• If not Skittles®, then it
doesn’t have an ‘S’ on it
• False!
Summary
• Conditional
– If a  then b
• Converse
– If b  then a
• Contrapositive
– If not b  then not a
• Inverse
– If not a  then not b
Summary
• Conditional
– If a  then b
• Converse
– If b  then a
• Contrapositive
– If not b  then not a
• Inverse
– If not a  then not b
Summary
• Conditional
– If a  then b
• Converse
– If b  then a
• Contrapositive
– If not b  then not a
• Inverse
– If not a  then not b