Geometry Chapter 02 A BowerPoint Presentation

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Presentation transcript:

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

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®, 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

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?

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

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 Is this true?

If Skittles®, then there’s an ‘S’ on it True! Conditional If a  then b If Skittles®, then there’s an ‘S’ on it True!

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®

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® Is this true?

If there’s an ‘S’ on it, then Skittles® False! 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 Combined into a biconditional statement: 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.

(Remember to use IF AND ONLY IF) 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

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®

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® Is this true?

If there’s not an ‘S’ on it, then not Skittles® 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

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

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 Is this true?

If not Skittles®, then it doesn’t have an ‘S’ on it False! Inverse If not a  then not b If not Skittles®, then it doesn’t have an ‘S’ on it False!

Summary Conditional Converse Contrapositive Inverse If a  then b If b  then a Contrapositive If not b  then not a Inverse If not a  then not b

Summary Same true or false Conditional Converse Contrapositive Inverse If a  then b Converse If b  then a Contrapositive If not b  then not a Inverse If not a  then not b

Summary Same true or false Conditional Converse Contrapositive Inverse If a  then b Converse If b  then a Contrapositive If not b  then not a Inverse If not a  then not b Same true or false