Transcript Indirect Proof

Indirect Proof
Objectives:
1. To write indirect
proofs
Assignment:
• Indirect Proof
Worksheet
Objective 1
You will be able to write
indirect proofs
Indirect Proof
Assume the Given
information is true
and use deductive
reasoning to reach a
true conclusion in
the form of the
Prove statement
Assume the Prove
statement is false
and use deductive
reasoning to reach a
contradiction
Direct Proof
Indirect Proof
Proof by Contradiction
Negate the Prove
statement and use
it as your Given
information
Find a contradiction
If your assumption leads to
a contradiction, then the
original Prove statement
must be true
Assume the Prove
statement is false
and use deductive
reasoning to reach a
contradiction
Indirect Proof
I heard from Hagrid
that it might be
raining tonight.
It must be raining.
If it wasn’t raining,
then people
coming in to the
library would be
dry, but they are
all wet.
Example 1
In your group, come up with a real-life
example of indirect proof, an instance when
you have proven something by contradiction.
That’s Not Rational!
Indirect proof is commonly illustrated by
proving that 2 is not rational.
A number is
rational if and
only if it can be
written as a
ratio of
integers 𝑎/𝑏,
𝑏≠0
Two numbers
are relatively
prime, or fully
reduced, if and
only if they have
no nontrivial
factors in
common
A number is
even if and
only if it can be
written as 2𝑘
for some
integer 𝑘
That’s Not Rational!
Example 2
Given: 𝑊𝑇 ≠ 𝑇𝑆
Prove: Quad 𝑊𝐼𝑆𝐻 is not
a parallelogram
Procedure
Assume the opposite of the Prove statement
Deduce a contradiction
State that this contradicts some know fact
Conclude that the original Prove statement must be true
Example 3
Given: 𝑚∠1 > 𝑚∠2
Prove: 𝑙 ∦ 𝑚
Example 4
Given: 𝑛 is odd
Prove: 𝑛 is not divisible by 4
Example 5
Given: 𝑚∠𝑁 ≠ 𝑚∠𝑂
Prove: 𝑁𝑇 ≠ 𝑂𝑇
Indirect Proof
Objectives:
1. To write indirect
proofs
Assignment:
• Indirect Proof
Worksheet