It's important to learn how to cut setting and corner triangles for on point quilts. These triangles are used to fill in the triangular gaps that occur along the outer edges of a quilt when blocks are sewn together in diagonal rows.
Straight set quilting layouts do not require triangles to connect the edges of quilt blocks.

Corner and Setting Triangles Look Alike but Are Cut in Different Ways
Two types of triangles are used for setting and corner triangles. Although they look alike, their structures are very different and they are cut in different ways.
 Triangles used in the four corners of a quilt have straight grain edges along their shortest sides.
 The straight grain flows parallel to the longest side of triangles used to fill in the remaining edges of the quilt top.
Why Does Fabric Grain Matter?
To minimize stretch, it's best to assemble quilt components with the fabric's straight grain along edges that will be on the outer perimeter of a block or quilt, so that there's less chance of stretch as you work.
That difference may not seem important, but makes a huge impact on the stability of the outer edges of your projects.
Using Quilt Blocks for Outer Triangles
Quilters sometimes opt to sew partial quilt blocks to use as setting and corner triangles. You'll find examples of that technique in Pitchers for Tildy's Cabin, shown here, and again in the Floating Nine Patch quilt.
Partial blocks used for setting components must be drafted especially for their spot in the quilt. You cannot cut patchwork setting triangles by dividing a block into halves or quarters because triangles produced with that method do not include extra seam allowances and will be too small.
It's easier and far more common to cut setting triangles from quilting fabrics.

How to Cut Corner Triangles
Corner triangles are halfsquare triangles that are created by cutting a square of fabric in half once diagonally to produce two triangles with the straight grain on their short edges.
The stretchy bias runs along a corner triangle's longest edge and becomes stabilized when it's sewn to a quilt block.
Corner Triangle Instructions
 Determine the size of the triangle needed by multiplying the finished block size by 1.41.
 Divide the answer, the finished diagonal, by 2.
 Add 0.875" and round up to the nearest 1/8" to find your parent block size.
 Cut two parent blocks that size and divide each in half once diagonally to make a total of four corner squares.
The tiny bit added when you round up is rarely noticeable when you sew the triangles to the ends of rows.
Parent Squares for Common Quilt Block Sizes
 4" blocks: cut 33/4" parent squares
 6" blocks: cut 51/8" parent squares
 9" blocks: cut 71/4" parent squares
 10" blocks: cut 8" parent squares
 12" blocks: cut 93/8" parent squares
 14" blocks: cut 103/4" parent squares
 15" blocks: cut 111/2" parent squares

How to Cut Setting Triangles
Setting triangles are quartersquare triangles that are created by cutting a square of fabric in half twice diagonally to produce four triangles with the straight grain on their long edge. That edge becomes the outer perimeter of a quilt unless borders are used.
If setting triangles were cut like corner triangles, their longest edges would flow along the stretchy bias, making the outer edges of a quilt more likely to stretch out of shape before the project is complete.
Setting Triangle Instructions
 Multiply the finished block size x 1.41.
 Add 11/4" to the dimension calculated in Step 1 and round up to the nearest 1/8".
 Create a square with sides that match the calculated size.
 Cut the square in half twice diagonally. You may need to carefully rotate the fabric after making the first cut to avoid cutting backward with a rotary cutter, an unsafe move.
Parent Squares for Common Quilt Block Sizes
 4" blocks: cut 7" parent squares
 6" blocks: cut 93/4" parent squares
 9" blocks: cut 14" parent squares
 10" blocks: cut 153/8" parent squares
 12" blocks: cut 181/4" parent squares
 15" blocks: cut 221/2" parent squares