Experimental tools to model cell-tissue interactions will likely lead to new ways to both understand and treat cancer. While the mechanical properties and regulation of invasion have been recently studied for tumor cells, they have received less attention in the context of tumor vascular dynamics. In this article, we have investigated the interaction between the surfaces of structures encountered by endothelial cells invading their surrounding extracellular matrix (ECM) during angiogenesis. For this purpose, we have fabricated round and sharp geometries with various curvature and sharpness indices in collagen hydrogel over a wide range of stiffness to mimic different microenvironments varying from normal to tumor tissues. We have then cultured endothelial cells on these structures to investigate the bi-directional interaction between the cells and ECM. We have observed that cell invasion frequency is higher from the structures with the highest sharpness and curvature index, while interestingly the dependence of invasion on the local micro-geometry is strongest for the highest density matrices. Notably, structures with the highest invasion length are linked with higher deformation of side structures, which may be related to traction force-activated signaling suggesting further investigation. We have noted that round structures are more favorable for cell adhesion and in some cases round structures drive cell invasion faster than sharp ones. These results highlight the ability of endothelial cells to sense small variations in ECM geometry, and respond with a balance of matrix invasion as well as deformation, with potential implications for feedback mechanisms that may enhance vascular abnormality in response to tumor-induced ECM alterations.