It is not a science, it is a form of mathematics. The suffix "-metry" often refers to mathematics, "-ology" refers for a type of science.
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Geometry is not a science but it is exact.
That depends on its application in science or geometry which has not been given. In science it can turn light into different colours and in geometry it can be in the form of a triangular prism.
Plane geometry.
analytical geometry
Geometry, unlike science, doesn't really have laws, it has theorems, and many different mathematicians contributed to the creation of the basic theorems of geometry. Perhaps the best known is Pythagoras.