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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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