Chapter 5 Parallel Lines and Related Figures

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Presentation transcript:

Chapter 5 Parallel Lines and Related Figures 5.1 Indirect Proof Learner Objective: Students will prove statements using "Indirect Proof".

Warm-Up Prove: Given: M is the midpoint of Learner Objective: Students will prove statements using "Indirect Proof". Warm-Up Given: M is the midpoint of Prove: D A C B M

Either ________ or _________. Learner Objective: Students will prove statements using "Indirect Proof". Given: Either ________ or _________. Assume _________. From the given information, Prove: A B C Thus, But this contradicts D E F Therefore, my assumption was false and  _________, because this is the only  other possibility.

Indirect Proof Template Learner Objective: Students will prove statements using "Indirect Proof". Indirect Proof Template Either or What you want to prove Opposite of what you want to prove. Assume Opposite of what you want to prove. We know from the given information that We know that Thus Then A chain of conclusions and reasons until you  reach an impossibility. This will be a contradiction  of either (a) given information or (b) a theorem, definition, or other known fact. But this contradicts The know fact that has been contradicted. Therefore my assumption was false and because this is the only other possibility. the statement you have proved

Indirect Proof Procedure: Learner Objective: Students will prove statements using "Indirect Proof". Indirect Proof Procedure: 1. List the possibilities for the conclusion. 2. Assume that the negation of the desired conclusion is correct. 3. Write a chain of reasons until you reach a contradiction of   a. Given information or   b. A theorem, definition, or other known fact. 4. State the remaining possibility as the desired conclusion.

We know from the given information that Then But this contradicts Learner Objective: Students will prove statements using "Indirect Proof". Either or Assume  We know from the given information that  Then    But this contradicts  Therefore, my assumption was false and  since that is the only other possibility.

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof". Assignment  5.1: 1, 2, 5-12, 15

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".

Learner Objective: Students will prove statements using "Indirect Proof".