IfThen Statements Geometry Chapter 02 A Bower Point

If-Then Statements Geometry Chapter 02 A Bower. Point 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