How would you right a proof for this theorem: "If a segment is given, then it has exactly one midpoint"? Please note that the numbering of the postulates (P) is based on my geometry book. Also, I'm just in 9th grade geometry, so please don't use differential equations or some other math than basic Euclidean geomtery. This will help me better understand the concept. This is what I did so far: This is where I kind of get lost.... Does that prove Q is the midpoint? I don't think so because: 1.) I haven't shown that the arithmetic I did in an attempt to show the distances between AQ and BQ are equal to that of AB works for all cases. 2.)I'm not sure I have adequately proven that A, Q and B are on the same line.