Why is equal terminal resistance sufficient for circuit equivalence?

[arpon]

To prove the wye-delta transformation formula, it is said 'If the two circuits are to be equivalent,
the total resistance between any two terminals must be the same.' But why ? I can't convince myself that it is sufficient condition for the equivalence of circuits.

 

[zoki85]

To prove the wye-delta transformation formula, it is said 'If the two circuits are to be equivalent,
the total resistance between any two terminals must be the same.' But why ? I can't convince myself that it is sufficient condition for the equivalence of circuits.

In order to input/output currents for given voltage be the same. What else did you expect to mean by the equivalence of the circuits?