Overlaping triangles

shahar

shahar

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If I have 3 angles and an area that is constant number, can I create different triangle with them that aren't overlapping?
 
I'm not sure what you mean by "overlapping"; but if you know the three angles, then the shape is determined, and then the area will determine the size, so any triangles that satisfy the data will be congruent, and in that sense not different.
 
Yes I was confused by replacing the word congruent with the word overlapping/
Are there proofs to it?
 
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So you meant, are there any non-congruent triangles with the same angles and area.

I outlined a proof, in explaining why this would be true! If you want to fill out the details, just think for yourself. I mentioned similar triangles (same shape); can you find theorems about that? Then can you see why only one of a set of similar triangles can have a given area?
 
shahar said:
If I have 3 angles and an area that is constant number, can I create different triangle with them that aren't overlapping?
Click to expand...
following suggestion in response #(4)

Which theorem is pertinent here (Hint : ASA)
 
There are two steps to my outline. Do you see the first? Please tell us whatever you do understand about this.
 
I think about rectangle that if I know side and area I can find the other size and its always congruent rectangle. I know that the forumla: 0.5(hight*size) like the rectangle. Am I in the course to solution?
 
It's related, at least. If you know the base (which is one side) and area of a triangle, then you can find its height. You need to see that if you also know the angles, then this is enough to determine all the sides (and therefore determine a single triangle).
 
shahar said:
I can't see the proof, still...
Click to expand...
Consider triangles with the same angles. If you scale one to make it larger or smaller, what happens to its area? Can it stay the same?
 
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