If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.
-
Upload
allyssa-brackenridge -
Category
Documents
-
view
216 -
download
0
Transcript of If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.
![Page 1: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/1.jpg)
If-Then Statements
Geometry
Chapter 02
A BowerPoint Presentation
![Page 2: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/2.jpg)
Conditional
• If a then b
• Hypothesis is a
• Conclusion is b
![Page 3: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/3.jpg)
Conditional
• If a then b
• If Skittles®, then there’s an ‘S’ on it
• What is the hypothesis?
![Page 4: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/4.jpg)
Conditional
• If a then b
• If Skittles®, then there’s an ‘S’ on it
• What is the hypothesis?–If Skittles
![Page 5: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/5.jpg)
Conditional
• If a then b
• If Skittles®, then there’s an ‘S’ on it
• What is the conclusion?
![Page 6: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/6.jpg)
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
![Page 7: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/7.jpg)
Conditional
• If a then b
• If Skittles®, then there’s an ‘S’ on it
• Is this true?
![Page 8: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/8.jpg)
Conditional
• If a then b
• If Skittles®, then there’s an ‘S’ on it
• True!
![Page 9: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/9.jpg)
Converse
• If b then a
![Page 10: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/10.jpg)
Converse
• If b then a
• If there’s an ‘S’ on it, then Skittles®
![Page 11: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/11.jpg)
Converse
• If b then a
• If there’s an ‘S’ on it, then Skittles®
• Is this true?
![Page 12: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/12.jpg)
Converse
• If b then a
• If there’s an ‘S’ on it, then Skittles®
• False!
![Page 13: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/13.jpg)
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…
![Page 14: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/14.jpg)
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.
![Page 15: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/15.jpg)
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)
![Page 16: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/16.jpg)
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
![Page 17: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/17.jpg)
Contrapositive
• If not b then not a
![Page 18: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/18.jpg)
Contrapositive
• If not b then not a
• If there’s not an ‘S’ on it, then not Skittles®
![Page 19: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/19.jpg)
Contrapositive
• If not b then not a
• If there’s not an ‘S’ on it, then not Skittles®
• Is this true?
![Page 20: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/20.jpg)
Contrapositive
• If not b then not a
• If there’s not an ‘S’ on it, then not Skittles®
• True!
![Page 21: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/21.jpg)
Inverse
• If not a then not b
![Page 22: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/22.jpg)
Inverse
• If not a then not b
• If not Skittles®, then it doesn’t have an ‘S’ on it
![Page 23: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/23.jpg)
Inverse
• If not a then not b
• If not Skittles®, then it doesn’t have an ‘S’ on it
• Is this true?
![Page 24: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/24.jpg)
Inverse
• If not a then not b
• If not Skittles®, then it doesn’t have an ‘S’ on it
• False!
![Page 25: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/25.jpg)
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
![Page 26: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/26.jpg)
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
![Page 27: If-Then Statements Geometry Chapter 02 A BowerPoint Presentation.](https://reader036.fdocuments.net/reader036/viewer/2022070307/551b023f5503462e578b5292/html5/thumbnails/27.jpg)
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