The Gettysburg quilt block pattern will give you lots of practice using half square triangles in different ways, rather than the most common patch made by using two contrasting right angled triangles to make a square.
*Note: More famous places (and not so famous) quilt block links are at the bottom of this post.
This nine patch quilt block makes wonderful use of the square in a square patch, in two different colourways. The careful placement of the triangles in the square in a square patch results in a star formed in the centre of the block.
The two sample quilts illustrated are very different looking — but both are generated using the same quilt block. Your imagination in action will come up with all sorts of interesting designs of your own.