Anonymous asked in Education & ReferenceHomework Help · 1 decade ago

How do you write geometry proofs?

i have to write a proof for geometry class.

The textbook says to write a proof

given blah

and prove blahblah

blah is just something

so can i write a two column proof

or do i have to write a paragraph?

thats all im asking

and how to write a paragraph proof too.


5 Answers

  • Sa T
    Lv 5
    1 decade ago
    Favorite Answer

    Given that the sum of the internal angles of a parallelogram is 360 deg., Show that the sum of the internal angles of a triangle is 180 deg.

    Proof: By adding lines parallel to 2 of the sides of the triangle, drawn from the 2 apexes, you obtain a parallelogram whose diagonal is the third side. Because of symmetry , you have 2 similar triangles because they have 2 sides parallel to each other and one side in common. Therefore each will have angles whose sum is half of that of the parallelogram. 360/2=180 Q.E.D.

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  • Anonymous
    1 decade ago

    Two column proofs are the least-used type of proof in actual mathematics because the format is so very rigid. That rigidity is also why they're the first type we teach - it's much easier to teach something with specific rules, and it's much easier for a student to see what they're doing wrong when you can say "the reason you supplied was not 'given', a definition, a postulate or a theorem".

    As to whether you are allowed to write a two-column proof instead of a paragraph, that's up to your teacher. What did she tell you? If no instructions were given, then it's up to you. Write it as you wish.

    Writing a paragraph proof is in some senses easier than writing a two-column proof, but it's also harder to get it right. The overall idea is the same in all proofs: never make a statement without backing it up with solid reasoning. In a paragraph proof, you can occasionally relax the "always give a reason" rule, especially for things like givens and definitions, but it takes some time to learn where you can leave them out and where you can't. That's especially true because for every case of one person saying "that's obvious, you can leave it out", there will be at least one other person saying "it's not that obvious to ME". Judgment comes into play.

    If you're going to write a paragraph, start by stating the facts as you know them. Draw whatever immediate conclusions you wish to from them, stating the reasons clearly, and continue on until you've proved what you want to prove. To quote Lewis Carroll in slightly different circumstances, "Begin at the beginning. Move on to the end. Then stop."

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  • Anonymous
    1 decade ago

    Hahaha, proof sucks. If it doesn't clarify then it means to write a 2 column proof. And a paragraph proof is just a 2 column proof in paragraph form (personally I find these easier).

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  • sander
    Lv 4
    3 years ago

    i do no longer fairly understand what an oblique evidence is however the clues you like are those to procure interior the above answer. regardless of the incontrovertible fact which you do no longer understand the right degree of perspective A. You do know it fairly is no longer 60 levels via fact, via fact the angles interior a triangle upload as much as one hundred eighty levels and perspective B is a hundred and twenty, then that basically leaves 60 levels for the relax 2 angles. So angles A and C jointly are 60 levels. btw - it is a possibility to have a nil degree perspective (leaving the different 60 levels for the 2d perspective), yet you will no longer be able to create any shape with a nil degree perspective. :)

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  • Anonymous
    1 decade ago

    Proofs are in two columns

    Statements | Reasons

    The first statement is the given information and the first reason is always "given"

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