Everything You Need to Know about Triangles in Quilting:
Questions 1: What kind of triangles are Half & Quarter Square Triangles?
Question 2: How can you tell Half Square Triangles from Quarter Square Triangles in blocks like these?
Question 3: How much seam allowance do you need to add to the finished size to make Half and Quarter Square Triangles, using a quilt ruler alone? It's great to know this if you want to make accurate half square triangles and quarter square triangles.
Question 1: What kind of triangles are Half & Quarter Square Triangles?
1. Isosceles Triangles
Right Isosceles Triangles
Actually answers 1, 2 and 3 are all correct. Both Half and Quarter Square Triangles have two equal sides and two equal angles making them Isosceles Triangles. But they also both have one right (90°) angle making them Right Triangles. So the most complete definition is that they are both Right Isosceles Triangles.
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!
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.
Question 3: How much seam allowance do you need to add to the finished size to make Half and Quarter Square Triangles, using a quilt ruler alone?
Almost every one answered 7/8" for Half Square Triangles and 1 ¼" for Quarter Square Triangles, which is correct. But what most quilters don't know today is those numbers are actually rounded up. So while it's true that every pattern and every instruction book today adds 7/8" and 1 ¼", that's because rulers only have lines every 1/8".
Everyone knows that the end result is to have an extra ¼" around each piece.
When you cut a square in half to make two Half Square Triangles, you create two more edges that also have to have an extra ¼" for the seam allowance. If you do the math, to get an exact 1/4" around all six edges of two Half Square Triangles, the precise answer is 0.854".
And for an exact ¼" around all twelve edges of four Quarter Square Triangles the exact answer is 1.207". Since you can't find those lines on a ruler, they get rounded up to 7/8" (0.875") for Half Square Triangles and 1 ¼" (1.25") for Quarter Square Triangles.
If you have an old rotary cutting instruction book from the early 1980's, it will most likely tell you that the numbers for triangles have been rounded up. They used to recommend lining up a little short of the line when making triangles and you'll even find a few quilters today that recommend adding 1 3/16" for Quarter Square Triangles, which is a little closer to 1.207". But most quilters today have never even heard that the numbers are off a little so they just think that they aren't cutting them accurately.
That's one reason the different brands of paper templates that have you sew on the lines and then tear the paper away work better. You do have the extra step of tearing the paper out, but they eliminate the built-in error you get when using a quilt ruler alone.