Using a nonseparable variable approach, the electronic energy spectra and wave-functions of 2D triangular quantum structures, including the hemi-equilateral triangle, the isosceles triangle, and the equilateral triangle are deduced and analyzed. The exact and analytical electronic states and energy-level equations in the three types of triangular structures are obtained. Numerical calculations are performed based on the material parameter of typical AlN semiconductor. The energy-level structures and wave-function distributions of electronic states are discussed in detail. The result reveals that the symmetry of the triangular quantum structure plays an important role in the energy-level structures and wave-function distributions of the triangular quantum structures