I am using layer cake squares to make this block, though you could cut the 10" squares yourself from fat quarters or yardage. The first step is to divide your layer cake squares into pairs of a light and dark color (or two contrasting colors such as blue and gold, or red and green - here, I am using light and dark). Using a rotary cutter and long ruler, cut each pair of squares diagonally twice, as shown.
Separate the four quarters, and keeping the two pieces together, cut across each triangle pair with a ruler and rotary cutter, 2.5 inches from the longest side.
Now, switch the pieces and sew the light colored small triangle to the dark colored trapezoid and the dark triangle to the light trapezoid. To sew, line up the pieces, right sides together, so the points of the bottom edge of the triangle like up with outer edge of the top of the trapezoid. Press the seams (I pressed mine open). It will not look exactly right as the trapezoid extends beyond the edges of the triangle - see the photo.
The next step is to take care of that wonkiness by trimming. I used a 9.5" square ruler. (You can use a different size but I found 6.5" was too small.) Line up a corner of the square ruler with the 90 degree corner of your two-part triangle and trim off the parts of the trapezoid that fall outsdie the edges of the ruler. You now have perfect right triangle.
Sew two trimmed right triangles together a shown below, matching seams. It is important to match the seams where the light and dark colors come together, rather than matching the ends of the pieces. Handle and sew carefully, as you are dealing with a bias edge. Press the seams carefully so you don't stretch your fabric.
Sew two of these units together, so all of one color comes together in the center (light in this case) and the other color forms the outer edge (dark here). It looks more complicated than it is! The last step is to trim the dog ears at the corners.
Here is an alternative setting for the blocks.
I'll show you the progress I've made on this quilt next week.