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If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.

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1 If-Then Statements Geometry Chapter 02 A BowerPoint Presentation

2 Conditional If a  then b Hypothesis is a Conclusion is b

3 Conditional If a  then b If Skittles®, then there’s an ‘S’ on it What is the hypothesis?

4 Conditional If a  then b If Skittles®, then there’s an ‘S’ on it What is the hypothesis? –If Skittles

5 Conditional If a  then b If Skittles®, then there’s an ‘S’ on it What is the conclusion?

6 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

7 Conditional If a  then b If Skittles®, then there’s an ‘S’ on it Is this true?

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

9 Converse If b  then a

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

11 Converse If b  then a If there’s an ‘S’ on it, then Skittles® Is this true?

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

13 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…

14 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.

15 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)

16 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

17 Contrapositive If not b  then not a

18 Contrapositive If not b  then not a If there’s not an ‘S’ on it, then not Skittles®

19 Contrapositive If not b  then not a If there’s not an ‘S’ on it, then not Skittles® Is this true?

20 Contrapositive If not b  then not a If there’s not an ‘S’ on it, then not Skittles® True!

21 Inverse If not a  then not b

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

23 Inverse If not a  then not b If not Skittles®, then it doesn’t have an ‘S’ on it Is this true?

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

25 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

26 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

27 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


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