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Prove geometric theorems Videos 4 videos

Formal Proofs
1858 Views

Formal proofs present the oh-so-mathematical evidence in two columns: one for the statement they are claiming is true, and the other for the reason...

Indirect Proofs
1734 Views

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 ar...

Conditional Statements
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If you already know what a conditional statement is, then you're smarter than you look. And boy do you look smart.

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Indirect Proofs 1734 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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