Here is a sample sketch that displays what I'm talking about:
The most obvious way of making a square is to independently cut two triangles out of different pieces of fabric and sew those triangles together to form a square. Of course, apart from being the most obvious, this is the most time-consuming and problematic way of preparing quilt squares.
If you take two triangles of fabric and simply sew them together, chances are you won't get a perfect square. And you need more than one square for a quilt. So on top of the fact that your squares might be uneven, they might be uneven each in a slightly different way. So when it's time to put them together, you end up stretching here and hiding there just to make pieces come together.
There are a few better ways of making triangles, but for today, I'll just describe one -- the one I believe is the easiest.
First of all, take two square pieces of fabric.
Turn the second piece upside down and place it directly on top of the first piece (the one on bottom should be face up). Make sure you align them properly; you can use pins to secure the pieces together.
Mark three lines on the back of the second piece. First one will be the line where you cut your fabric -- a diagonal from corner to corner (black line). Then, mark two lines where you'll sew the fabric (yellow lines) -- make them 1/4" away from the center line.
Once aligned, sew through the fabric (both pieces) in place of where you would have sewing markers (the yellow lines). After that, cut the pieces in place of the diagonal (the black line).
Cut the leftovers so they don't stick out. (I'm only showing one folded triangle out of two you would have at this moment.)
Unfold the triangles into squares. The leftover 1/4" is on the back side as it's supposed to be. And you have two squares.
There is one thing to note. Since you are sewing around 1/4" off the diagonal, your resulting squares will be smaller than the original ones. There is a geometrical function, according to which, the resulting square will have it's sides' length shorter by "the square root of eight times the size of the marker offset squared." For 1/4", the side will be smaller by 0.71" or a little under 6/8". So make sure to make your original squares that much larger than the desired size of the resulting triangle squares. Sorry if that sounds a bit confusing. Simply stated: if you space 1/4" away from the diagonal, you need to subtract 6/8" from the length of a side of the original square to get the length of a side of the resulting one.
Another way to know what size to cut squares to make 1/2 square triangles is add 7/8" to the finished size. For instance, if you want a finished 1/2 square of 2" cut your original two colors at 2 7/8" squares and then sew as you direct. (Using Triangles on a Roll is also a huge time saver if you're making lots of blocks and works on the same principal as this method.) There is a great book out, Patchwork Minus the Mathwork, that costs about $8 and is worth every penny. Give these kinds of figures and lots, lots more. I have it refer to it often.
I like this method for making half sq. triangles best. The only thing I do to further simplify is that I cut the squares 1" larger than I want the finished hal-sq. triangle square to be. This way I have a little extra to trim off after sewing and pressing to have PERFECTLY sized squares and I don't have to deal with measuring 1/8" anywhere.
Another hint, that I was given was to iron the squares open and then refold to cut them apart as this helps to keep them square as sometimes ironing them after cutting can cause distortion because of the bias.
I would like to add a tip that I was taught about quarter square triangles and half quare triangles. To the size of a the triangle you want to make add 1 1/4 inches. Example: if you want a 6 1/2 triangle (finish size 6 inch) add 1 1/4 Inch to it then the size will be 7 3/4 inches sew mark and sew like explained in todays newsletter. When you are done sewing it take a 6 1/2 square ruler (it should have an X drawn on it as to center it to your sewn square they are also known as "squaring" rulers) center the ruler with the center of the sewn square and cut around it. voila! one finished triangle