High Quality Content by WIKIPEDIA articles! In geometry, the segment addition postulate states that if B is between A and C, then AB + BC = AC. The converse is also the same. If AB + BC = AC, then B is between A and C. The segment addition postulate is used a lot in proofs involving the congruence of segments. Visualize that XY and WZ intersect each other with V being the point of intersection. Let's say that segment WV is congruent to segment VY and that segment XV is congruent to segment VZ. That's our given, and we want to prove that segment XY is congruent to segment WZ. The first step to take involves using the segment addition postulate. We can say that XV + VY = XY and WV + VZ = WZ both by the segment addition postulate. The next step involves getting XY = VZ + WV by the substitution property. Since XY and WZ both equal WV + VZ, we can get XY = WZ by the substitution property. Thus, segment XY is congruent to segment WZ by the definition of congruent segments.

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