ShmoopTube

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

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

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

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

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burger and french fry companies pay Olympic athletes to advertise their

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stuff even mathematicians worshippers of logic and reason contradict themselves

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from time to time hopefully these contradictions are only

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

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

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

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

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

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

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

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

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

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

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

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other we know that perpendicular segments make

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right angles so angle ABC must be a right angle

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

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

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degrees but statement 5 says it's 90 degrees

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

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dimension so we've contradicted ourselves since we

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

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

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

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

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

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