Final answer:
The claim is true; two segments EF and GH in the plane are congruent if they have the same length, as congruence in geometry is defined purely by the measurement of length.
Step-by-step explanation:
The statement "If EF is a piece of string in the plane, and GH is a piece of string in the plane with the same length as EF, then EF is congruent to GH" is true. In geometry, two segments are considered congruent if they have the same length, regardless of their position or orientation in the plane. The fact that EF and GH are both strings and are on the same plane is less relevant than their lengths for determining congruence. Therefore, as long as the lengths of EF and GH are identical, the two segments are indeed congruent.
To illustrate this, let's assume EF has a length of 5 units and so does GH. According to the definition of congruence in geometry, these two segments are congruent because their lengths are equal. We do not need to consider other properties such as their location or orientation in the plane to conclude their congruence.