We study the plasmon resonances for small two-dimensional silver particles (nanowires) with elliptical or triangular shapes in the 20 nm size range. While the elliptical particle has only two resonances, a well known fact, we demonstrate that the triangular particle displays a much more complex behaviour with several resonances over a broad wavelength range. Using animations of the field amplitude and field polarization, we investigate the properties of these different resonances. The field distribution associated with each plasmon resonance can be related to the polarization charges on the surface of the particles. Implications for the design of plasmon resonant structures with specific properties, for example, for nano-optics or surface enhanced Raman scattering are discussed.