When a router running EIGRP considers alternate paths, which ones will it consider loop-free?

An RD equal to the FD does not satisfy the Feasibility Condition (the condition requires strictly less than, not equal to), so equal-RD neighbors are not guaranteed to be loop-free and are not classified as Feasible Successors.

The EIGRP Feasibility Condition states that a neighbor is a Feasible Successor (loop-free alternate) only when its Reported Distance (RD) - the neighbor's own best metric to the destination - is strictly less than the local router's Feasible Distance (FD), the best known metric. This guarantees the neighbor is topologically downstream and cannot route back through the local router, mathematically eliminating routing loops.

A route whose feasible distance equals the best possible route describes the Successor (current best path), not the criteria used to identify loop-free alternate Feasible Successors.

An RD equal to the metric of the best path means RD equals FD, which fails the strict less-than requirement of the Feasibility Condition and does not guarantee a loop-free path.