Anonymous
Anonymous asked in Education & ReferenceHomework Help · 1 decade ago

A better understanding of Geometric Proofs and Theorems.?

I have the worst understanding of Proofs and its theorems and I do not understand how to order them properly. I only learned about parallelograms, quadrilaterals, triangles, squares, rhombuses and rectangles, and so far I don't understand anything.

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  • 1 decade ago
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    Hahah everyone hates proofs...

    Alright the first thing you have to write is what you're given

    Given:

    (Shape) ABCD, Angle of __ = Angle of __, ect... (whatever it gives you)

    Then what you're trying to prove

    Prove: __

    Now depending on the type of proof they're solved differently.. but i'll assume you're talking about (paragraph/ table) proofs.

    Always start body with "It is given that___(restate your givens)__"

    Next figure simply use mathematical theorems to prove what you're attempting to prove. With the shapes that you've mentioned the things you're going to need to look for are CONGRUENT/ SIMILAR TRIANGLES, AND PARALLEL LINES.

    This is incredibly hard to show you without a diagram, but here's a great proof that should help you.

    http://www.algebra.com/algebra/homework/Parallelog...

    Just remember that if triangles are congruent then they all sides are equal.

    Corresponding Parts of Congruent Triangles are Equal (CPCTE theorem)

    remember ASA AAS SSS and SAA all make the triangles congruent.

    SSA and AAA do NOT necessarily make triangles similar

    Alternate interior, Corresponding, Alternate exterior, angles are equal when a transversal intersects two pairs of parallel lines.

    Verticle angles are equal

    Reflexive property of equality

    Substitution

    Distributive property of equality

    and know the definitions of parallelograms quadrilaterals triangles squares rhombuses and rectangles.

    Knowing just those you can solve virtually any geometric proof. sorry i can't really go into more detail it's hard to be so general (every proof is different) if you'd like to post an example I'd happily help you solve it. =D

    Well hope this helps.. Good luck with geometry!!

  • 4 years ago

    If you have an inequality, you can always add any term to both sides and keep the inequality. In this case, 4ab is what is necessary to be added to change (a-b)^2 into (a+b)^2.

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