Where do you find elements grouped that have the most similar physical and chemical properties?

The chemical properties depend on the number of valence shell electrons since these electrons participate in chemical bond formation with other elements. The elements are arranged in the periodic table in such a way that the elements having same number of electrons in the valence shell are grouped together.  

Therefore the chemical properties of the elements present in the same group are similar. As for example the halogens (Group VII) made up of fluorine, chlorine, bromine, iodine and astatine. In fact since they all seven electrons in the valence shell they are therefore called halogens. All halogens exhibit similar chemical properties. It is true for all other groups.  

The physical properties like melting point , boiling point partially depend on the valence shell and it also depends on the type of interactions between the atoms of the element. Thus to some extent it shows similarity along a group.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y

answergravity;