Question 177641: How do I write an indirect proof? What are the steps to writing an indirect proof? How do I set up an indirect proof?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! check this website out.
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http://www.icoachmath.com/sitemap/IndirectProof.html
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there are others.
just go to yahoo or google and search on: geometry indirect proof
or: indirect proof
or: indirect proof method
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you prove something indirectly by assuming that it is false and then showing that the assumption that it is false leads to a contradiction in terms of known facts or postulates or previously proven theorems.
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the website i sent you to has 2 examples.
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the steps are the same as in proving directly, except the logic progression goes down until you reach a statement that is clearly false.
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for example, the second example in the website i sent you to proves that a triangle can have at most 1 right angle by assuming that it has 2 and then showing that this yields to a contradiction in what is already known, namely that the sum of the angles of a triangle = 180 degrees.
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prove:
triangle has at most 1 right angle
assume:
triangle has more than 1 right angle.
show this is impossible in light of the fact that:
sum of angles of triangle = 180.
each angle of triangle has to be more than 0 degrees.
steps:
triangle abc has 2 right angles.
let angle a = right angle
let angle b = right angle
right angle = 90 degrees
angle a + angle b = 180 degrees
since sum of angles of triangle must = 180, this means that angle c = 0 degrees.
since the angles of a triangle must be greater than 0 degrees, this is a contradiction meaning that the triangle cannot have more than 1 angle of 90 degrees meaning that the triangle can have at most 1 angle of 90 degrees meaning that the triangle can have at most 1 right angle.
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