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Tue 29 Aug, 2006 10:50 am
I was going over geometric proofs last night just for fun and began to ask myself several questions.
I want to ask you the same questions.
Can I proof geometric shapes using numbers in terms of coordinate geometry?
For example:
If I am given that side AB = 10 and that side BC = AB, prove that triangle ABC is isosceles.
I should be able to proof that this is an isosceles triangle without having to use the statement vs reason chart. Am I making sense?
Take this one:
Given side AB is 9cm and side BC does equal side AB, prove that triangle ABC is NOT isosceles. Do you what I mean?
I think geometric shapes can be proven simply using numbers in place of the famous statement vs reason chart.
It is a MILLION times easier for me to proof geometric shapes using numbers in place of words. Agree?
This statement vs reason chart is only necessary to learn if I am going to teach high school math someday in a classroom. See my point?
I have seen MANY college geometry exams and never did I ONCE face a geometric proof question using the statement vs reason chart like they teach in high school.
What do you think?
shark
The whole point about a "proof" is that it is universal...not particular to one case. For example in algebra it is not sufficient to "prove" an identity by showing "it works" for some chosen numbers. This is also the case in geometry. Indeed the primary pedagogical (teaching) purpose of "geometry" is to exercise general reasoning skills...set thory or mathematical logic would equally serve that purpose.
BTW your second example may still be an isosceles triangle because you fail to define the third side.
Quote:Given side AB is 9cm and side BC does equal side AB, prove that triangle ABC is NOT isosceles. Do you what I mean?
No I don't know what you mean because this triangle must be isosceles.
What is a statement vs reason chart anyway?
stuh505
I think he meant to say ".....and BC does NOT equal AB"
I assumed a "statement versus reason chart" was a fancy description of a conventional line by line proof. i.e. each line of proof consitutes a STATEMENT followed by a REASON for its validity. This might end say with a satisfaction of three congruence conditions thereby proving a fourth pair of items are equal. This could all be formatted as a table.
Oh, ah, ok. Well in that case, shark, there is no avoiding the statement vs reason table because ANY valid proof can be written in that fashion. You can use geometry or whatever, and as long as you do it correctly, it can be written in this chart. It is more common to put the reasons inbetween the lines as explanations in natural language.
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