What does work for blocks like these, and the most common answer given is by which way the grain line of the fabric runs.
This is a great answer because it works for almost any block or unit in quilting.
We all know that in quilting you never want a bias edge that can stretch out of shape on the outside of a block or unit. We always start by first squaring up our fabric, so that we cut our strips on the straight grain.
Knowing this makes it so much easier to tell Half & Quarter Square Triangles apart.
When you look at each individual patch with triangles in it, if the short sides of the triangle are on the outside, it is a Half Square Triangles. And if the long side is on the outside, it is a Quarter Square Triangles.
Now you can even tell them apart in trickier blocks and units.
- Flying Geese unit: You want the grain line of the finished unit to run straight up and down and side to side. You see the short sides of the two yellow triangles on the outside, so they are Half Square Triangles.The long side of the pink triangle is on the outside, so it's a Quarter Square Triangle. You can watch an animation explaining this by clicking here.
- Brave New World block: You see one large triangle and two smaller ones. But, if you ignore the difference in size, you can see that the short sides of all the triangles are on the outside, so they must all be Half Square Triangles.
- Square-in-a-Square unit: An interesting thing about this unit is that the center square is on point, meaning that the grain line is running diagonally. If left that way, it is going to stretch out of shape. Surrounding it with Half Square Triangles solves the problem because their short sides: the straight grain line, is now on the outside of the unit and that prevents the finished unit from stretching out of shape.. Yay!
About Quilt Blocks on Point:
So now that you've got all the right triangles in all the right places so there are no bias edges on the outside of your block. Let's rotate them all 45 degrees and set them on point. Now all the bias edges are running straight up and down and side to side!
It's triangles to the rescue again. We always use Side and Corner Setting Triangles when we set blocks on point. When you look at the Corner Setting Triangles, you see that their short edges are on the outside so they are Half Square Triangles. The long edges of the Side Setting Triangles are on the outside so they are Quarter Square Triangles.
The bottom line is that now the outside edges of you finished quilt top is "set" with the grain line running straight up and down and side to side, so your quilt will hold its shape.