Liquids show different static wetting morphologies in open triangular grooves depending upon the wedge angle (ψ) of the groove and the liquid contact angle (θ) with the substrate. Switching between different morphologies can be achieved either by varying the contact angle of the liquid or by changing the wedge angle of the groove. In the present work we manipulate the apparent contact angle of a liquid by electrowetting to switch between liquid morphologies, from droplet to filament, to achieve microfluidic transport of the liquid into open triangular grooves. The static length of liquid filaments in grooves is analyzed as a function of applied voltage for different applied ac frequencies. The dynamic advancement of the filament lengths in grooves is analyzed as a function of time for different applied voltages for two different liquids: first with contact angle greater than the wedge angle and second with contact angle smaller than the wedge angle. Later an exact electrical model is derived to explain the liquid transport in triangular grooves actuated by electrowetting which includes the precise geometry of the liquid morphology.