if-then statements geometry chapter 02 a bowerpoint presentation

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