Cutting perfectly sized half-square triangles used to be a challenge until I learned this simple trick. Start by aligning your ruler diagonally across the square from corner point to corner point. Holding the ruler in place, look just to the inside of the ruler edge instead of along the outside edge. Chances are you will find that you are not exactly across the points but slightly to one side. Adjust the ruler accordingly. Verify the alignment and cut. The result is evenly cut half-square triangles.
Why does this work? The ruler acts much the same as the support posts in a windshield. Although the post itself may be narrow, it effectively blocks a sizable object from view. A rulers outer edge does the same thing. Happy Quilting! Sharon