Chapter 5 Parallel Lines and Related Figures 51 Indirect Proof Learner Objective Students will prove statements using Indirect Proof WarmUp M is the midpoint of Given Prove D A C B ID: 248006
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Learner Objective: Students will prove statements using "Indirect Proof".
Chapter 5 Parallel Lines and Related Figures
5.1 Indirect ProofSlide2
Learner Objective: Students will prove statements using "Indirect Proof".
Warm-Up
M is the midpoint of
Given:
Prove:
D
A
C
B
MSlide3
D
E
F
A
B
C
Given:
Prove:
Learner Objective: Students will prove statements using "Indirect Proof".
Either ________ or _________.
Assume _________.
From the given information,
Thus,
But this contradicts
Therefore, my assumption was false and _________, because this is the only other possibility.Slide4
Learner Objective: Students will prove statements using "Indirect Proof".
Indirect Proof Template
What you want to prove
Opposite of what you want to prove.
Opposite of what you want to prove.
Either
or
Assume
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
Therefore my assumption was false and
because this is the only other possibility.
The know fact that has been contradicted.
the statement you have provedSlide5
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.Slide6
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.Slide7
Learner Objective: Students will prove statements using "Indirect Proof".Slide8
Learner Objective: Students will prove statements using "Indirect Proof".
Assignment
5.1: 1, 2, 5-12, 15Slide9
Learner Objective: Students will prove statements using "Indirect Proof".Slide10
Learner Objective: Students will prove statements using "Indirect Proof".Slide11
Learner Objective: Students will prove statements using "Indirect Proof".Slide12
Learner Objective: Students will prove statements using "Indirect Proof".Slide13
Learner Objective: Students will prove statements using "Indirect Proof".Slide14
Learner Objective: Students will prove statements using "Indirect Proof".Slide15
Learner Objective: Students will prove statements using "Indirect Proof".Slide16
Learner Objective: Students will prove statements using "Indirect Proof".Slide17
Learner Objective: Students will prove statements using "Indirect Proof".Slide18
Learner Objective: Students will prove statements using "Indirect Proof".Slide19
Learner Objective: Students will prove statements using "Indirect Proof".Slide20
Learner Objective: Students will prove statements using "Indirect Proof".Slide21
Learner Objective: Students will prove statements using "Indirect Proof".Slide22
Learner Objective: Students will prove statements using "Indirect Proof".Slide23
Learner Objective: Students will prove statements using "Indirect Proof".Slide24
Learner Objective: Students will prove statements using "Indirect Proof".Slide25
Learner Objective: Students will prove statements using "Indirect Proof".Slide26
Learner Objective: Students will prove statements using "Indirect Proof".Slide27
Learner Objective: Students will prove statements using "Indirect Proof".Slide28
Learner Objective: Students will prove statements using "Indirect Proof".Slide29
Learner Objective: Students will prove statements using "Indirect Proof".Slide30
Learner Objective: Students will prove statements using "Indirect Proof".Slide31
Learner Objective: Students will prove statements using "Indirect Proof".Slide32
Learner Objective: Students will prove statements using "Indirect Proof".Slide33
Learner Objective: Students will prove statements using "Indirect Proof".Slide34
Learner Objective: Students will prove statements using "Indirect Proof".