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Indirect Proofs 1732 Views


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Description:

Indirect proofs (or proofs by contradiction) prove their conclusion by showing that the opposite cannot be true. You can use this in math and in arguments with your siblings.

Language:
English Language

Transcript

00:03

indirect proofs a la shmoop from one point of view the world is a [Young girl looks through binoculars]

00:09

bucket of hypocrite or contradictions green-friendly rock stars begged the

00:14

world to donate to the poor and support our environment but fly in to their

00:18

concerts on vastly expensive gas guzzling jets we want to be in shape but [Jet lands on runway]

00:23

burger and french fry companies pay Olympic athletes to advertise their

00:27

stuff even mathematicians worshippers of logic and reason contradict themselves

00:32

from time to time hopefully these contradictions are only

00:36

in indirect proofs an indirect proof or proof by contradiction is a type of

00:42

argument that proves its conclusion by showing that the opposite cannot be true

00:47

talk about meaning around the bush let's say that segments AB and CD are

00:53

perpendicular and we're asked to prove that angle ABC is not a straight angle

01:00

you see the word not in the conclusion yeah that's a hint that you might want [Light bulb turns on]

01:05

to try using an indirect proof first thing we do is take our conclusion and

01:10

assume the opposite that it is true so in this case we assume that angle ABC is

01:16

a straight angle now let's find that contradiction we'll start with our

01:21

assumption that angle ABC is a straight angle straight angles are 180 degrees in [A protractor appears]

01:26

measure so the measure of angle ABC is 180 degrees go with us on this now let's

01:34

use what we're actually given segments AB and CD are perpendicular to each

01:40

other we know that perpendicular segments make

01:43

right angles so angle ABC must be a right angle

01:47

all right angles are 90 degrees in measure so angle ABC must have a measure

01:53

of 90 degrees too... hold on a minute statement 2 says that angle ABC is 180 [Statement 2 highlighted from table]

01:59

degrees but statement 5 says it's 90 degrees

02:02

there's no way both statements can be true at the same time in our same

02:06

dimension so we've contradicted ourselves since we

02:10

made an assumption that resulted in a contradiction we know our assumption has

02:13

to be false so we can conclude that angle ABC is not a straight angle it may

02:20

have been indirect but we finished the job we've fixed our contradiction and [Man and woman arguing and young girl smiles]

02:24

done what we set out to do now all that's left is to fix that ozone layer

02:28

hopefully sooner than later one [Plaster appears over planet earth]

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