- Thread starter shahar
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And if you are asked about symmetry of a figure, you need to look at it, not to draw it for yourself.

But maybe some of the theorems used to prove constructions can also be used in a proof of symmetry ...

Can you give an example of such a problem, and how you want to answer it?

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"Show

As you say: There is

So, we (the solvers of such kind of problems) can't go further/deeper to do it (in advance (???)), Right?

My original question was about clues that helps to show it. Cause that using compass and straightedge are only to draw. Or I am wrong?

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A compass and straightedge construction can find the line of symmetry between two opposite points on wings, and then find the reflection of any given point on one side, to show that that corresponds to a point on the other side. Enough such points can build evidence for the conclusion -- not a deductive argument, but sort of an inductive one.

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Now, it happens that I initially wrote that "nothing in nature" has perfect symmetry, but changed that to "no living thing". Why? Because I thought of crystals. Even they are probably never exactly what they "ought" to be, though. Why? Randomness.