The half-square triangle, or right angle triangle, may be the workhorse in traditional patchwork design but we shouldn’t overlook other types of triangles. ** Equilateral**,

**,**

*scalene***and**

*acute*

*obtuse***can add drama and excitement to our quilts. I suspect some of these types of triangles are used less frequently because they are not as easy to rotary cut and piece. But with specialty rulers, templates or paper foundation piecing, they can be sewn just as easily and successfully as half-square triangles.**

*triangles***Equilateral Triangles**

An equilateral triangle, or a *regular* triangle, has three sides of equal length and three equal interior angles of 60°.

When I think of equilateral triangles in quilts, I think of *Thousand Pyramids*. As I was doing a little research into this quilt design, I realized that it isn’t limited to equilateral triangles – any isosceles triangle will do. That is to say, it requires *two *sides of equal length, not necessarily three. Nevertheless, let’s take a look at *Thousand Pyramids* and some of its variations.

In this first example, equilateral triangles are sewn together into rows. The second and alternating rows are mirror images of the first row. The upward pointing triangles are one color and the downward pointing triangles another.

Another option is to color opposite triangles in such a way as to form diamonds. This version is sometimes called *Tumblers*, although tumblers can also be a different shape altogether.

By off-setting the rows of triangles, *Thousand Pyramids* becomes *Lightning. *In this coloration, with the dark triangles pointing down and the light triangles pointing up, a *Dog’s Tooth* design is created.

But by coloring the upward-pointing and downward-pointing triangles as a row, you get the *Streak of Lightning* effect.

**Scalene Triangles**

A scalene triangle has three unequal sides. The interior angles may vary, but for quilters one of them is usually 90°.

This block is called *Double Z* and it has both scalene and isosceles triangles. The light and dark violet patches are the scalene triangles.

Often, scalene triangle patches are found in blocks where a rectangular patch is divided in half diagonally. Such is the case in this *Nosegay* block.

This example is just full of scalene triangles. The block is called *Cool Fan* – just what we need in this summer heat!

**Acute and Obtuse Triangles**

These triangles are identified by their interior angles. An acute triangle has three interior angles that are less than 90° whereas an obtuse triangle has one interior angle which is greater than 90°.

Many of the scalene triangles in the examples above are also acute triangles. Patchwork blocks with obtuse triangles tend to also have acute triangles – which makes sense when you think about it. In *The Priscilla* block, obtuse triangles fill in the space formed by the acute triangles.

I really like the look of this block set on point.

nice

If the scalene triangle has a 90-degree angle, you can use the Pythagorean theorum of a-squared + b-squared = c-squared. “a” and “b” are the two sides that form the 90-degree angle. If your Bird of Paradise block is based on a nine-patch grid, “a” would equal one-third of the block size and “b” would be half of “a”. A picture would be worth a thousand words here, so let me know if this isn’t making sense and I’ll post an article on it in the future.

If you use EQ design software, you could also use the Print Rotary Cutting feature. Set your block size and EQ will tell you exactly how to rotary cut each patch. Good luck!

How do I mathematically figure out how to make a scalene angle cut for my bird of paradise block without using a template to do it? Thank you.