The Half Square and Flying Geese components are some of the most used components in quilting.  So WHY do the pattern makers keep using the techniques that require us to cut triangles? Using triangles create a huge potential to have your component go wonky.....that #$%$# bias! Plus that's a lot of cutting when I had rather be sewing!

When I open a new pattern, the first thing I do is scan for these two components and see how the pattern designer has approached them. If the pattern calls for cutting triangles for a half square unit or flying geese unit, I literally tell the pattern - no, not now, not ever! NOW, it's important that you make this decision before you cut any fabric!
Then I just do some simple math and cut my fabric so that I can use Eleanor Burn's method. Eleanor uses two squares of fabric to make 2 half square triangles and two squares to make 4 flying geese.  SQUARES---that don't require you to worry about that bias stretch. AND all the points come out perfect every time.  
We have taught this for years in our Saturday Sampler class - So here's two YouTube videos we made to teach the techniques for Flying Geese and Half Square triangles.