How can you use the segment addition postulate to show that ae=ab+bc+cd+de

First, we differentiate the definition of a line and a line segment. A line is a series of points that are connect together which extend infinitely at both ends at straight directions. A line segment is a portion of a line. It does not extend infinitely because it has two points along the line as its ends. 

Knowing the definition of a line and line segment, it would be easier to understand the Segment Addition Postulate. It states that in a line AC, if point B lies along the line, then that means that AB + BC = AC. The line segments within that line should add up together. Therefore, we can apply this postulate to line AE shown in the picture. Since points B, C, and D are in between the line, then that means AE=AB+BC+CD+DE.