Final answer:
The question appears incomplete and is related to congruence in geometry and vector addition, but without further context or diagrams, it is challenging to address the specifics of the students' statements or the calculation related to the farmer's plot of land.
Step-by-step explanation:
The rather complex question involves understanding congruent triangles, properties of polygons, and vector addition. The student provides information on congruent triangles in a context that implies geometric optics, and vector addition related to force or velocity diagrams.
However, the initial question seems incomplete or fragmented. The provided statements, such as AB = EF or AD + GF, are not sufficiently contextualized to verify their truth without additional diagrams or descriptions of points E, F, G, and H. Nevertheless, geometry and congruence rules apply to determine that, if triangles are congruent, their corresponding sides and angles must be equal.
The discussion on farmer fencing a plot of land suggests the application of vector addition to close a polygon. The formula y + A + B + C + D = 0indicates that when vectors representing the sides of the plot are added head-to-tail, they should form a closed shape, which is analogous to the sides of the plot summing to zero when considering direction.