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**Geometry Chapter 02 A BowerPoint Presentation**

If-Then Statements Geometry Chapter 02 A BowerPoint Presentation

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Conditional If a then b Hypothesis is a Conclusion is b

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**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?

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**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

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**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?

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**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

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**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?

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**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!

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Converse If b then a

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**If there’s an ‘S’ on it, then Skittles®**

Converse If b then a If there’s an ‘S’ on it, then Skittles®

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**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?

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**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!

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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…

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**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.

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**(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)

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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

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Contrapositive If not b then not a

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**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®

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**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?

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**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!

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Inverse If not a then not b

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**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

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**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?

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**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!

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**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

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**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

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**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

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