Edge detection is a vital step in image processing, pattern recognition and computer vision. While edge detection were tackled on the traditional rectangular and on the hexagonal grids, there is a lack of studies on the triangular grid. In this paper, we fill this gap, we adapt various classical edge detection techniques and algorithms into the triangular grid. We start by gradient-based technique, where we introduce filters on the triangular grid corresponding to the Sobel filter on the square grid. We also discuss the second-derivative operators such as Laplacian filter as well as some low pass filters, such as Gaussian smoothing, allowing us to derive the Canny and Laplacian of Gaussian filters. We adapt these techniques keeping in mind the properties, the topology and neighborhood of the triangular grid with some modifications to the filters for improved results. Some filters give more accurate edges while some others have nice properties like robustness to noise. By our results, the Laplacian filter gives the best results on denoised images, while the Prewitt-T and Canny-T filters give good results on noisy images on the triangular grid.