SSS, ASA, SAS ProofsDate: 01/21/2002 at 18:08:09 From: Sarah Subject: Proofs Dear Dr. Math, Hello! I know you've answered a lot of questions about proofs, but I'm still having trouble with them. Can you please explain them in fuller detail? My problem is that I understand the ideas, but I'm not sure when and where to use them. I especially need help with SSS, ASA, SAS, etc. I get confused with what they mean and how to tell which one is which. Thank you, Sarah Date: 01/21/2002 at 23:37:04 From: Doctor Peterson Subject: Re: Proofs Hi, Sarah. I assume you have looked through the Dr. Math FAQ on Proofs: http://mathforum.org/dr.math/faq/faq.proof.html and have read problems like these: Congruent Triangles in a Rectangle http://mathforum.org/dr.math/problems/lacey.11.11.99.html Writing a Proof http://mathforum.org/dr.math/problems/tony.05.16.01.html Triangle Proof http://mathforum.org/dr.math/problems/ashley.11.19.01.html Congruent Parts Congruent Triangles Congruent (CPCTC) http://mathforum.org/dr.math/problems/brittany.11.28.01.html Here is a quick summary of what each method of proof means: SSS SAS ASA + + + / \ / \ / \ c/ \a c/ \ / \ / \ /A \ /A C \ +-----------+ +-----------+ +-----------+ b b b + + + / \ / \ / \ c/ \a c/ \ / \ / \ /A \ /A C \ +-----------+ +-----------+ +-----------+ b b b All three sides Two sides and Two angles and of one triangle the included the included agree with all angle of one side of one three sides of triangle agree triangle agree the other. with the other. with the other. One way to think of it is to say that, if you were given one of these three sets of three numbers, it would be enough to be able to draw that triangle correctly. For example, If I told you angle A and sides b and c, you could draw line b, make a ray A degrees from it, and measure c units along that ray. Then you would have all three vertices of the triangle, and would know that you had exactly the shape I had in mind. If I just gave you, say, the three angles, you would have to choose a length for the sides, so you would not be sure. That's why there's no AAA congruence theorem. The answers I recommended show how to use these in practice. If you find that you have the appropriate set of congruent pairs of parts between two triangles, then you can use that theorem to say they must be congruent. If you need more direct help, please write back and show me a sample problem that gave you trouble, so I can see where you get confused and suggest specific ideas. You can also find more examples at this ThinkQuest site: Geometry: Congruent Triangles - Math for Morons Like Us http://library.thinkquest.org/20991/geo/ctri.html - Doctors Peterson and Sarah, The Math Forum http://mathforum.org/dr.math/ |
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