GM-U1.8 Lesson: Indirect Proofs

Multiple Choice

ACT Prep Warm-Up:

Statement 3 will be: $$m\angle EBA=m\angle1+m\angle2$$ what reason could I give for the statement I chose?

• Substitution w/ 1,2

• Definition of an angle bisector.

• Definition of congruent.

• Definition of midpoint.

Unit 1 Lesson 8:
Indirect Proofs

Assume that what you want to prove is false, which should lead to a contradiction. Therefore proving the original statement true.

​Indirect Proof

Concepts:

A logical operation that reverses the truth value of a statement.

​Negation

A statement that conflicts with itself or with established fact.

Contradiction

Concepts:

Procedure: Negated Conclusion

1) Assume the conclusion is false.
2) Negate the conclusion.
3) Test the conditional w/ the negated conclusion.
4) If a contradiction arises the original statement was true.

Procedure: Contrapositive

1) Assume the conclusion is false.
2) Write the contrapositive of the conditional.
3) If the contrapositive is true the original statement is true.

Example 1:

Conditional Statement: If an animal is a zebra, then it cannot fly.

Contradiction:







Contrapositive:

Example 2:

Conditional Statement: If the product of two integers is odd, then each integer is odd.

Contradiction:







Contrapositive:

Example 3:

Complete the conditional statement using indirect reasoning:

Every student in Mr. Evans' 4th hour class got an A on the Geometry test. Jess got a B on the test.

Indirect Reasoning:

Multiple Choice

If a conditional statement is true, what other statement must also be true?

• Contrapositive

• Inverse

• Converse

• Intrapositive

Multiple Choice

Select the term that best matches the definition:

"A logical operation that reverses the truth value of a statement."

• Negation

• Inversion

• Conversion

• Positron

Multiple Choice

Select the term that best matches the definition:

"A statement that conflicts with itself or with established fact."

• Negation

• Inversion

• Conversion

• Positron

Open Ended

Negate the following conditional and explain whether or not this creates a contradiction: If today is Friday, then tonight there is a football game.

Open Ended

Negate the following conditional and explain whether or not this creates a contradiction: If tomorrow is not Thursday, then today is not Wednesday.

Open Ended

Write the contrapositive of the following conditional and determine whether the statements are valid: If the product of two integers is negative, then the signs of the integers are mixed.

Open Ended

Write the contrapositive of the following conditional and determine whether the statements are valid: If the whole numbers between 1 and 4 are 2 and 3, then both are factors of 6.

Open Ended

Complete the conditional statement using indirect reasoning:

Only students who studied at least 3 hours for the Geometry test got an A on it. Joey studied 2 hours for the test.

Indirect Reasoning: .........