Almost all of the patchwork / quilt blocks consist of squares and half triangle squares. Cutting and sewing each of these components individually can seem like a pain, when you have a large project in hand. But it is not rocket science to make these half triangle squares in no time.

The obvious way of sewing these half-triangle squares is to cut squares first of both the colors – you will be cutting from two types of fabrics – one a background fabric and another a contrasting colored fabric.
Cut the squares 1/2 inch bigger than the final square you want; ie if you want a 3 inch half triangle square cut 2 squares of 3 1/2 inches sides.

Then cut these squares by the middle diagonally. You get 4 triangles. Now join two of the triangles together – making your half triangle square.

But there is another easier speedier way. This is to cut your squares after sewing them.
Cut two coloured squares are usual.
Now Keep the two pieces – one dark and one background squares – one on top of the other( Right sides together to the inside.)

Mark a line diagonally as in the picture below along the middle (from one corner to the other)

Sew 1/4 inches to either side of this line – ie you will be sewing diagonally across the block in a straight line on either side of the middle line, from one corner to the other.The line you marked is the cutting line.

Cut along this line.
Separate your triangles.

Press open the seam allowance. Cut the extra corners of the seam allowance projecting outside.
There your 2 half triangle squares are ready with just one stitching. You can many the same way in no time.

A star quilt block is one very easy block that you can make with these half square triangles.

Check out this post on the 9 different types of star patchwork blocks that you can sew with the half triangle squares.
Related posts : Different types of quilt blocks ; Quilt vocabulary ; How to sew a 9 patch quilt block.