if-then statements geometry chapter 02 a bowerpoint presentation
TRANSCRIPT
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