symmetry principles always tell us something important. They often provide the most valuable clues toward deciphering the underlying principles of the cosmos, whatever those may be. In this sense, therefore, symmetry is certainly fruitful. Whether or not some all-encompassing symmetry is the grand principle that will necessitate our "theory-of-everything" is still to be determined.
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Line symmetry.
z does not have a line of symmetry. z does not have a line of symmetry. z does not have a line of symmetry. z does not have a line of symmetry.
Bilateral symmetry.
Mollusk have bilateral symmetry
An isosceles triangle has one line of symmetry, which is drawn from the noncongruent side to the opposite vertex, and does not have a rotation symmetry.