2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155117This is the first of two papers which aim to understand quasi-isometries of a subclass of unimodular split solvable Lie groups. In the present paper, we show that locally (in a coarse sense), a quasi-isometry between two groups in this subclass is close to a map that respects their group structures.48 pages (10pt, wide textwidth), 8 figuresMetric Geometrytext