Proving R is an Equivalence Relation on R^2

[jaejoon89]

A relation R on R^2 is defined by $$(x_{1},y_{1})\mathit{R}(x_{2},y_{2})\;\;\;if\;\;\;x_{1}^{2}+y_{1}^{2}=x_{2}^{2}+y_{2}^{2}$$

How do you show that R is an equivalance relation?

 

[CaffeineJunky]

What is the definition of an equivalence relation? (I.e. what properties do equivalence relations have over normal relations?)