Just found this online:
Perpendicular Bisector TheoremLet's talk perpendicular bisectors. These lines are immensely useful. Let's say you're an architect. I wanted to be an architect once. Then I realized it was less building cool models and more building regulations and codes. Anyway, let's completely ignore building codes here.Here's some land. You're designing a skyscraper. The folks who hired you made two demands: it needs to go straight up and it needs to be in the middle of the land. Seems simple enough, right?Say, do you know what you did? You made a perpendicular bisector. And it's not as simple as it seems. Consider the Leaning Tower of Pisa. Maybe it bisects the plots of land. But it definitely isn't perpendicular. Granted, who would visit the perpendicular tower of Pisa? These folks definitely ignored some building codes.Anyway, perpendicular bisectors come with their very own theorem. The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints. In other words, if we hung laundry lines from any floor of our tower, each floor would use the same length of laundry line to reach the ground. Okay, but I'm guessing the neighbors might complain about all the underwear hanging outside our tower