Geometry Section 5.4

Geometry Section 5.4

Inverses and Contrapositives

​Writing the negation of a statment.
Writing the inverse and converse of a statement.
Using indirect reasoning.

Goals:

Match

Match the following

• $$\sim p$$  

• $$\sim q$$  

• $$p$$  

• $$q$$  

Negation of the hypothesis

Negation of the conclusion

Hypothesis

Conclusion

• Negation of the hypothesis

• Negation of the conclusion

• Hypothesis

• Conclusion

Multiple Choice

Which statement is the negation of the statement:

Roses are red

• Violets are blue

• Red is not a nice color

• Roses are not red

• Roses are flowers

Multiple Choice

Which of the following is the negation to the statement,
"The stars shine at night."?

• In the day, the stars shine.
• At night, the stars shine.
• The stars are shining at night.
• The stars do not shine at night

Multiple Choice

Given the following statement find the converse.

If I go then you stay.

• If you stay then I go

• If I stay then you go

• If I don't go then you don't stay

• If you don't stay then I don't go

Multiple Choice

Given the following statement find the inverse.

If I go then you stay.

• If you stay then I go

• If I stay then you go

• If I don't go then you don't stay

• If you don't stay then I don't go

Multiple Choice

Given the following statement find the contrapositive.

If I go then you stay.

• If you stay then I go

• If I stay then you go

• If I don't go then you don't stay

• If you don't stay then I don't go

​Logically Equivalent

• ​If the conditional statement is true then the contrapositive must be true.

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• ​Likewise, if the converse is true the inverse must be true.

​Logically Equivalent

• ​If the conditional statement is false then the contrapositive must be false.

​

• ​Likewise, if the converse is false the inverse must be false.

Multiple Choice

When the conditional statement is false, which other statement must be false

• inverse

• converse

• contrapositive

Multiple Choice

When the inverse statement is false, which other statement must be false

• conditional

• converse

• contrapositive

Multiple Choice

Find the contradiction given triangle ABC.

I. ABC is isosceles

II. Angle A is obtuse

III. Angle B is a right angle

• I and II

• I and III

• II and III

Multiple Choice

Find the contradiction given quadrilateral BLUE.

I. BLUE is a square

II. BLUE is a rectangle

III. Sides BL and LU are not equal.

• I and II

• I and III

• II and III

Formative 5.4

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Homework