cutting into 4 makes 1/4 square triangles- not half square triangles. and doing it that way gives you 2 bias edges to deal with which makes very unstable blocks to work with- there are much better ways to make these-
1/2 square triangles you cut your squares- put two together- draw a diagonal line- stitch 1/4" on each side of the line- then cut on the line for (2) 1/2 square triangle blocks.