The replacement of delta meshes by equivalent star systems is known as delta-star transformation.

Consider the two systems shown in

These two systems will be equivalent or identical if the resistances measured between any pair of lines are same in both of the systems, when the third line is open.

Hence resistances between terminals B & C

= R₃(R₁+R₃)  in delta system
   R₁+R₂+R₃
and = R_B+R_C in star system

Since the two systems are identical, therefore, resistance measured between terminals B and C in both or the systems must be equal.

R_B+R_C = R₃(R₁+R₂)
             R₁+R₂+R₃

Similarly resistance between terminals G and A being equal in the two systems:

R_C+R_A = R₁(R₂+R₃)
             R₁+R₂+R₃

and resistance between terminals A and B

R_A+R_B = R₂(R₁+R₂)
               R₁+R₂+R₃

Adding equations (i), (ii) and (iii) we get

2(R_A+R_B+R_C) = 2(R₁R₃+R₂R₃+R₁R₂)
                              R₁+R₂+R₃

or   R_A+R_B+R_C = 2(R₁R₃+R₂R₃+R₁R₂)
                                 R₁+R₂+R₃

Subtracting expressions (i), (ii) and (iii) from expression (iv) we get

        R_A =      R₁R₂  
                 R₁+R₂+R₃

        R_B =    R₂R₃    
               R₁+R₂+R₃

and  R_C =     R₃R₁   
               R₁+R₂+R₃

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