This seems backwards to me. It's not as though things "line up" magically, but rather there's enough "wiggle room" to allow things line up. It's similar to me

This seems backwards to me. It's not as though things "line up" magically, but rather there's enough "wiggle room" to allow things line up. It's similar to me to saying that given three non-negative integers A, B, and C, you can form a triangle with side lengths A, B, and C if and only if the sum of any two numbers is greater than the third. "Why" this is the case is best understood by seeing what happens when it doesn't hold. Or, another way would be to take two line segments attached at the end, fix one, and rotate the other. As you rotate, draw a line between the endpoint of one segment and the other. The range of lengths of this third side is going to be the permissible range of lengths for any third side length and it's going to be "largest" when the two original line segments have a 180º angle between them (i.e., their sum). But I think for plenty of people this wouldn't suffice to answer the question "why." It could still seem like a "happy accident." This is always the tricky thing with why questions -- what constitutes an explanation for one person is entirely unsatisfactory to another.