reason to have a marker in making a hst.
 

Why do I have to draw a line from corner to corner and then sew 1/4 inch on either side of drawn line. What happens if I just cut on a diagonal and sew fabric together?

You can do that too. Usually you have more control over the bias seam if you sew first then cut. Usually less distortion. If you are careful you can cut first. Try it and see how it comes out. If you are happy, then you can continue with that technique.

I have done the cut first way a few times with pretty good results. Pin, Pin, Pin. And sew slowly at first.

Bias edges stretch, easily. So if you cut first you have to be very careful sewing along that bias edge. The squares are just more stable. Many people prefer the stability and making two at a time instead of only one. If I were going to do them one at a time I would starch heavily before cutting and use pins.

I have done it both ways. I always have fear of the first, unsupported, edge will be drawn down into the needle hole-it has happened! So, if I do that, I leave a distance of a stitch or two from the corner, back stitch to the corner and move forward. That helps. It also helps to use a stitch plate for straight stitching. If I do the method that calls for sewing on either side of the drawn line, I sew them in the same direction. I chain piece all that I need to do, take the work out of the machine and go back to the first one and stitch the second line, I do not cut them apart until I have both sides done. I really feel that this cuts down on the wonkiness that some of us experience when making HSTs.

This is one of the reasons I find it easier and more accurate to sew first and cut second, but whatever works for you is fine. Sometimes I draw the center line and the stitch lines. Takes a little more time, but otherwise there are usually a few that are off that I need to redo, so may save me time overall. Something about sewing on a diagonal that makes it harder for me to sew straight.

As others have said - try it both ways and see which works out better for you.

I have cut and sewn many triangles that I cut using a template - which makes the triangle a "wee bit" bigger than if I cut a (finished size + 7/8 inch square) into triangles - and they turn out close to "expected" size.

Even when sewing what I consider "very scant" 1/4 inch seams with the (finished size + 7/8 square) - I almost always end up with skimpy units.

I

To stop that machine from "chewing" those triangle corners at the beginning of a triangle piece, use "leaders & Enders as per Bonny hunt/quiltvile

Additionally, you don't have to "draw" the line. You can press the square in half and use the press mark as a guide or you can use an awesome gadget called "Clearly Perfect Angles" http://www.newleafstitches.com/shop/...s-x8319256.htm
It is a plastic sheet that sticks to your machine bed and gives you a guide where to sew so you don't have to mark. I have one and love it.

I don't draw a line, I line up the corner with the line on my template attached to the machine bed.

http://i31.photobucket.com/albums/c3...psx2zkvhhn.jpg

When I'm going scrappy, I normally use my Easy angle to cut my triangles, I do not cut squares and then cut in half. I have absolutely no problem dealing with bias edges. I think it's because I had 30 years of garment construction under my belt before starting to make quilts. Quilting cotton fabric is about the easiest thing I can think of to sew.