
#2 Blocks are a little more challenging 

The Half Square Triangle Quilt Block
The half square triangle is one of the most popular quilt blocks. It is one of the foundation pieces of many quilt blocks.
The popularity of this quilt block, and the delicate diagonal grain line on the hypotenuse of the triangle, has lead to many shortcut methods of construction. Some of them involve using paper patterns or drawing them on paper.
There are several methods that I like. They are both frugal, easy, and involve making more than one triangle at a time.
To make the half square triangle you start out cutting squares. Working with squares or rectangles puts as little pressure as possible on the delicate and stretchy bias edges.
While you could sew triangles together, and with some blocks you do have to do that, when you work with squares it protects those bias edges so most quilters use this method.
HERE IS THE MOST IMPORTANT THING TO MEMORIZE WHEN IT COMES TO TRIANGLES, which will be explained below. 3/8 inch raw 7/8 inch finishedThe methods below will all be using the easy measurement of the 2 inch finished units.
METHOD
#1  The first method makes 2 half square triangles. You start by
cutting out 2 squares. Usually they are in a light fabric and a darker
fabric
You place them right sides together, and draw (or press) a diagonal line on one of the fabrics. Then you sew 1/4 inch on each side of the drawn line.
When you cut on the drawn line, you end up with 2 triangles.
As to measurements, you again use the 3/8 inch triangle measurement. As an example, if you want your raw half square triangle to measure 6 inches, you would cut your squares 6 3/8 inches.
However, if you want the finished size of the raw triangle to be 6 inches, you also have to add the seam allowance. So you would cut the squares at 6 7/8. (3/8 for the triangle, and 4/8 or 1/2 inch for the seam allowance).
You will hear the "add 7/8" more often, as patterns usually refer to finished size.
METHOD #2  This shortcut will yield 4 half square triangles. Cut 2 rectangles, one in the dark fabric, and one in the light fabric. Cut them 2 7/8 by 5 3/4 inches.
Draw a vertical line down the center of the rectangle, per the illustration. Then draw diagonal lines from the top center to the outside edges, again per the picture.
Sew 1/4 inch on each side of the diagonal lines.
Then cut on all the drawn lines
As you can see from the picture, when you pull them apart, you have 4 half square triangles.
Did you notice in the measurements above the 7/8 inch measurement? If you double 7/8 will come out with 1 3/4 inches. The width of two half square triangles (finished) is 4 inches. Add 1 3/4 inches to that and you get the measurement of 5 3/4 inches.
Again, remember with triangles the 3/8 raw and 7/8 inch finished measurements for calculating sizes.
METHOD #3 Again you put 2 pieces of fabric right sides together. However this time you draw 2 diagonal lines, as well as a vertical and horizontal line down the middle of the square.
Note: Use you iron and fold the piece in half for quick vertical and horizontal marks.
When you cut, not only do you cut on the diagonal lines, but you cut the piece in half vertically and horizontally.
As you can see when the pieces are pulled apart, this will give you 8 triangles.
METHOD #4  This shortcut method makes 8 triangles at one time, but differs from the other methods in that the squares are cut oversized, and you have to trim them.
However, this is a good technique to know, as it can use it to trim down any triangle to a smaller size.
Instead of using the exact measurement ( 5 3/4 inches), you cut the starting squares 6 inches. Again you put 2 pieces of fabric right sides together. Draw the lines as in method #3, and cut the fabric apart.
Here is how you square up your triangles.
First trim off the dog ears. You can cut them off before you open the triangle, as in the picture to the left, or you can wait until after you press open the triangle to clip them off.
Next, press the triangles. When you press the triangles, put the dark color on top. Use your fingers to press the triangle open, and then place the iron down for a few seconds.
Do not drag the iron across the triangle. Do not press more than once. Now you are going to need one of your square rulers to trim the half square triangle up to the right side.
This is one of the hardest steps for the new quilter. You need to line up 3 parts of your quilt block with 3 lines on the ruler.
Notice the vertical and horizontal black lines. The are both lined up at the 2 1/2 inch marks on the ruler. This is because the block is 2 1/2 x 2 1/2 inches.
The 45 degree line on the quilting ruler must also be placed on the seam of your block.
When all 3 of these things are lined up, you are ready to trim. Take your rotary cutter, and trim off all the fabric that is sticking out on top of the ruler, and to the left hand side of the ruler. This is where either a small cutting mat or one that turns comes in handy. You can just turn the mat to cut, without having to turn the block and line everything up again.
After you cut the fabric from the top and the side, your block should measure 2 1/2 x 2 1/2 inches. It takes some practice to trim, but you do get 6 triangles at one time.
You can use the above method of squaring up a block to cut down any triangle. For instance, if you have an 8 inch triangle that you want to make into a 6 1/2 inch triangle, just put your ruler over it as above, and cut it down.
Be sure to read the Piecing and Patchwork page, and look at strip piecing. When you speed up the cutting process by using this technique.
