diagonals

shahar

shahar

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Jul 19, 2018
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Is there a proof this if I had two diagonals of quadrilateral I know what is it?
If I had only 2 diagonals of pentagon I can also or I need 3?
Is there a polygon that I have minimum diagonals but not all of them I will know what it is?
 
As I understand this, you are asking,
  1. Is it true that the lengths of the two diagonals of a quadrilateral are sufficient to determine that quadrilateral. [NO]
  2. How many diagonals of a pentagon are sufficient to determine it?
  3. Something I can't interpret.
Before asking whether something can be proved, you should at least experiment with it, to see whether it seems likely to be true. Did you make any attempt to draw two different quadrilaterals whose diagonals are the same?

Similarly, can you make a guess, and support it with examples, as to whether 2 or 3 diagonals are enough to determine a pentagon? Just imagine arranging 2 or 3 sticks, and see whether moving them would change the resulting pentagon.

Then try to restate your third question.
 
shahar said:
Is there a proof this if I had two diagonals of quadrilateral I know what is it?
Click to expand...
No..

you need more parameters to ascertain the exact "quadrilateral".

You should know that three independent parameters for generalized triangle (ASA or SSS) are needed to prove uniqueness.
 
Last edited:
khansaheb said:
No..

you need more parameters to ascertain the exact "quadrilateral".

You should know that three independent parameters for generalized triangle (ASA or SSS) are needed to prove uniqueness.
Click to expand...
if I have the point that the diagonals meet each other - Can I know the quadrilateral that have them?
 
shahar said:
if I have the point that the diagonals meet each other - Can I know the quadrilateral that have them?
Click to expand...

shahar, no, and I will give a specific counterexample.

Let's be in the xy-plane. In the first case, look at two diagonals that are both 10 units long,
and they intersect at (0, 0). The endpoints of one diagonal are at (-4, 3) and (4, -3). The
endpoints of the other diagonal are at (-4, -3) and (4, 3). These diagonals correspond to a
rectangle that is not a square.

In the second case, we are still looking at two diagonals that are both 10 units long, and
they still intersect at (0, 0). However, the endpoints of one diagonal are at (0, 5) and (0, -5).
The endpoints of the other diagonal are at (-5, 0) and (5, 0). These diagonals correspond to
a square.
 
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