Any tromino (3 squares, joined edgewise) yields two ‘wedge’ shapes if you halve it by cutting the middle square diagonally. The wedges can be viewed as half-trominoes or as three 45-45-90 triangles aligned edgewise. Like the P-Pentomino, these wedges come in right- and left-handed forms which can tile themselves asymmetrically at a scale of 1/4.
Side lengths are 1, 1, √2 and 2. So for full plane tiling the non-integral side must align with the non-integral side of an adjacent wedge. Above are the shapes possible when two identical wedges are arranged edgewise. The chart below shows the ways two enantiomorphic wedges can be arranged edgewise.