How to Cut a Single Triangle
Quilting triangles are usually made by cutting up squares. There are a couple reasons for this. Usually you need two triangles, so there isn't any waste. However the main reason is that you want to avoid handling the bias as much as possible.
If you want a half square triangle, you cut a square once diagonally. If you want a quarter square triangle, you cut the square diagonally twice.
Half square triangles have the bias on the long side.
Quarter square triangles have two bias edges on the short sides.
The following instructions are for making half square triangles.
The pictures below are of the Spool and Bobbin quilt square. The Spool and Bobbin is a 4-patch quilt block that has been further divided into 16 patches. As you can see from the picture, each block has 2 large squares in the corners that cover 4 of the smaller patches.
The other 2 large squares contain the smaller patches. There are some shortcut methods to make these blocks, but for the purpose of cutting triangles we are going to do it the long way.
Focus on the top left quadrant of the square. You see a small square in the corner that has small triangles on each side of it, and a larger triangle on the bottom. Here is how you calculate the measurements for these pieces and put them together.
Beginning with the small square, you can see that it fills just one of the smaller grids. Planning each small grid to finish at 2 inches, these small squares are cut at 2 1/2 inches. This is half of the measurement of the large yellow squares, which are cut at 4 1/2 inches.
To calculate the size of the large blue triangles, take the finished size of the large square, and add 7/8 inches. Then cut it in half diagonally for 2 triangles.
To calculate the size of the small yellow triangles, take the finished size of the small square and add 7/8 of an inch. Cut it in half diagonally for 2 triangles.
When you added 7/8 of an inch to the size of the square, 1/2 inch is for the seam allowances. The additional 3/8 of an inch is for the seam between the triangles and the piece you will sew them to.
When attaching the small triangles to the square match the outer edges. The pointed part of the the triangle will extend beyond the seam line. Attach one triangle, press, and the do the other one. Trim edges even as you go.
When attaching the top unit to the bottom triangle, keep the top unit facing up when sewing so that you can see when you get to the middle of the seam. You want to sew right in front of the stitching line so that you do not cut off the point of the small triangle when it meets the large triangle.
You will not get into trouble cutting triangles as long as you remember the difference between raw and finished measurements, and use the 3/8 or 7/8 inch measurements.