Elucidating the rules for receptor triggering in cell-cell and cell-matrix contacts requires precise control of ligand positioning in three dimensions. Here, we use the T cell receptor (TCR) as a model and subject T cells to different geometric arrangements of ligands, using a nanofabricated single-molecule array platform. This comprises monovalent TCR ligands anchored to lithographically patterned nanoparticle clusters surrounded by mobile adhesion molecules on a supported lipid bilayer. The TCR ligand could be co-planar with the supported lipid bilayer (2D), excluding the CD45 transmembrane tyrosine phosphatase, or elevated by 10 nm on solid nanopedestals (3D), allowing closer access of CD45 to engaged TCR. The two configurations resulted in different T cell responses, depending on the lateral spacing between the ligands. These results identify the important contributions of lateral and axial components of ligand positioning and create a more complete foundation for receptor engineering for immunotherapy.