geometry:providing reasons to the statements in an arguement

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kissmass

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Oct 16, 2006
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ok. So there was this one problem that went like this:
Given: AL=SK
Prove: AS-LK

And the statements are provided for this problem. They are:

1. AL = SK
2. LS = LS
3. AL + LS = SK+LS
4. AL + LS = AS
5. SK + LS = LK
6. AS = LK

Now what I was supposed to do was provide the reasons for eeach step and this is what i have so far:

1. given
2. reflexive
3. ? substitution ?
4. & 5. i have multiplication as my answer but im not sure if its that, addition, or just simplifying

6. deffinition of comgruency


Im not sure what #'s 3, 4 & 5 would be and how you would figure out what it is.
im also not sure about #6..... so please help me. :lol:
 
Re: geometry:providing reasons to the statements in an argue

kissmass said:
ok. So there was this one problem that went like this:
Given: AL=SK
Prove: AS-LK
Click to expand...

Prove WHAT?
 
Re: geometry:providing reasons to the statements in an argue

kissmass said:
Given: AL=SK
Prove: AS-LK
Click to expand...
Even assuming you mean "Prove that AS = LK", it would be difficult to proceed, since we cannot see whatever picture you are looking at, which presumably displays the relationship(s) between A, K, L, and S.

Also please note that different geometry texts present different material in different orders, frequently using different names (and always using different numbering), so the best the tutors can do is provide general concepts; we cannot give you the specific property / axiom / postulate / rule / theorem number or name.

Thank you.

Eliz.
 
they tell u how they get the answer ur just supposed to give a reason for each step that u take.
 
kissmass said:
[T]hey tell [you] how they [got] the answer[; you're] just supposed to give a reason for each step that [they took].
Click to expand...
Yes, but without a clear statement of what, exactly, they were proving, there is no way for us to comment.

You can see the picture; you have the book with the listing of rules, theorems, axioms, properties, and the like. What are your thoughts? (Please use standard English when you reply.)

Thank you.

Eliz.
 
With the information provided it is possible to provide reasons for steps 1, 2, 3, and 6, but not necessarily for steps 4 and 5. You are correct in your responses for steps 1 and two, but not steps 3 or 6. Step 3 follows from steps 1 and 2 and the addition property. Given that AL = SK, adding equation 2 (LS = LS) gives you equation 3 (AL + LS = SK + LS). Another way of thinking about this is that adding LS to each side of equation 1 gives you equation 3.

The equation in step 6 follows from steps 3, 4, and 5 and the substitution property. Equation 4 states that AL + LS = AS, so AS may be substituted for AL + LS in equation 3. Similarly, equation 5 states that SK + LS = LK, so LK may be substituted for SK + LS in equation 3. Making these two substitutions results in equation 6.

Although stapel is correct in stating that more information about the picture is needed for us to be certain, it is possible to make some probable guesses about the reasons for steps 4 and 5 as well. If points A, L, and S are collinear and point L is between points A and S, it follows that AL + LS = AS (equation 4). Your particular geometry book will likely have a theorem stating this, and it may well be named the "betweenness of points theorem" or something like that. The same logic applies to step 5.

As I am new to this forum I am unsure whether or not to make you work or think a bit more to come up with your own answers based on some guiding thoughts or leading questions or if more directly stated answers as I have provided here are just as appropriate. Whichever the case, kissmass, may I suggest that are no shortcuts that allow success in geometry without a thorough knowledge and thoughtful application of the concepts found in the theorems, postulates, properties, and definitions that your textbook provides.

hreeve
 
hreeve said:
Although stapel is correct in stating that more information about the picture is needed for us to be certain, it is possible to make some probable guesses about the reasons for steps 4 and 5 as well.
Click to expand...
Agree, BUT if "guessing" is required, then there's something
wrong with the teacher that made up the problem :shock:
 
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