  We investigate equiangular lines in finite orthogonal geometries, focusing
specifically on equiangular tight frames (ETFs). In parallel with the known
correspondence between real ETFs and strongly regular graphs (SRGs) that
satisfy certain parameter constraints, we prove that ETFs in finite orthogonal
geometries are closely aligned with a modular generalization of SRGs. The
constraints in our finite field setting are weaker, and all but~18 known SRG
parameters on $v \leq 1300$ vertices satisfy at least one of them. Applying our
results to triangular graphs, we deduce that Gerzon's bound is attained in
finite orthogonal geometries of infinitely many dimensions. We also demonstrate
connections with real ETFs, and derive necessary conditions for ETFs in finite
orthogonal geometries. As an application, we show that Gerzon's bound cannot be
attained in a finite orthogonal geometry of dimension~5.
