The thousand pyramids quilts I've seen are based on equilateral triangles.
So - I will get to that -
The first drawing is a triangle in a square unit (Doreen Speckmann called them Peaky and Spike units) - the reason for showing that is that the sharper (more acute) the angle, the longer the 'tails' are when the seam allowance is added.
The lower three shapes are based on 60 degree (equilateral) triangles) The diamond shape has 60, 120, 60, 120 degrees angles and the triangle has 60, 60, and 60 degree angles.
The diamond and triangles are traced around templates from Pandora's Box as seen on Quilting from the Heartland, hosted by Sharlene Jorgenson.
The outside lengths of the equilateral triangle are longer by about 5/16 of an inch than the outside lengths of the diamond.
I rotary cut some paper shapes and used a ruler to mark 1/4 inch from the edge near the corner where the seams intersect. When using fabric, I usually use an ordinary lead pencil and make the marks just dark enough so I can see them. If using dark fabric, I use a 'silver' pencil or a chalk pencil.
I've found this to be helpful - even now - for getting triangles to line up correctly. A shortcut is to make a template the 'finished' size and just put that in the center of each piece and mark around the corners.