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Teachers & SchoolsIndirect 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.

Congruence | Prove geometric theorems |

Geometry | Logic and Proofs Prove geometric theorems |

Language | English Language |

Logic and Proofs | Formal (Two-Column) Proof Informal (Paragraph) Proof |

stuff even mathematicians worshippers of logic and reason contradict themselves

from time to time hopefully these contradictions are only

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

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

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

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

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

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

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

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

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

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

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

other we know that perpendicular segments make

right angles so angle ABC must be a right angle

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

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

degrees but statement 5 says it's 90 degrees

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

dimension so we've contradicted ourselves since we

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

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

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

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

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