It is of the essence of the procedure of measurement that the yard measure remains unaltered as it is transferred from one position to another.

Some objects can palpably alter as they move--for example, an elastic thread; but a yard measure does not alter if made of the proper material.

What is this but a judgment of congruence applied to the train of successive positions of the yard measure?
We know that it does not alter because we judge it to be congruent to itself in various positions.

In the case of the thread we can observe the loss of self-congruence.

Thus immediate judgments of congruence are presupposed in measurement, and the process of measurement is merely a procedure to extend the recognition of congruence to cases where these immediate judgments are not available.
Thus we cannot define congruence by measurement.
In modern expositions of the axioms of geometry certain conditions are laid down which the relation of congruence between segments is to satisfy.