Yes
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Yes it does. when tilted it has the same symmetric line.
A half moon has one line of symmetry. This line of symmetry divides the half moon into two equal halves that are mirror images of each other. The line of symmetry runs vertically through the center of the half moon, allowing both halves to be perfectly reflected across it.
The shape that has 1 curved side and 3 straight sides is a crescent. A crescent is a curved, closed shape that resembles a thin, partially illuminated moon. It is formed by the intersection of two circles or by removing a smaller circle from a larger one, resulting in one curved side and three straight sides.
Period of rotation is the time taken for an object to complete exactly one revolution around another object, like the earth rotating around the sun or the moon rotating around the earth.
At the moment of a lunar eclipse... the state when the earth, moon and sun are in direct alignment with each other. Details: At night, when a full moon is in the sky, and when the sun is directly behind the earth in line with the moon, and the shadow of the earth is projected onto the moon's surface.... "The earth together with its surrounding waters must in fact have such a shape as its shadow reveals, for it eclipses the moon with the arc of a perfect circle."~Nicolaus Copernicus. A similar effect can be observed during an annular eclipse of the sun, when the moon comes between the earth and the sun, obscuring the sun except for a bright ring of sunlight around the circumference.