The half square triangle unit is probably the most commonly used patch in a quilt block -- well it is second only to the square. It is made simply with two triangles, filling up half the square each -- hence the name. Take a quick look through this website, or in any quilting magazine, and you will start to notice that this half square triangle, regardless of its size, is present in more quilts than not.
Free Quilt Block Pattern
The Dancing Shoofly quilt block is new to me, and I always love to discover new blocks to play with.
This is one of those "block in a block" type of instances, because the centre of the quilt block is a separate block all on its own. Not to worry though, as it is all quite easy to construct this nine patch block, as it uses only squares, rectangles and flying geese patches.
I played around quite a bit with the sample quilts illustrated and had fun doing so. You will find the same thing when it is time for you to decide on your design layout. Enjoy!