Press K on the keyboard to bring out the knife tool. Cut across the plane from one vertex to another.

Nice edge established.

Press #2 at the top of the keyboard, not on the Numpad. #2 refers to edge mode. For instance, #1 as vertex mode, #2 as edge mode, and #3 as face mode.

Select two opposing edges and press the X key to bring out the sub-menu. Go down to where it says “Dissolve Edge” to get rid of the edges completely without affecting triangular faces. What will happen if you accidentally delete edges? The triangular faces will be deleted along with the edges you selected a moment ago.

And violas! Problem solved.
