Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
The Perpendicular Bisector Theorem states that for any given line segment, the perpendicular bisector of that segment will always pass through the midpoint of the segment, and will also be perpendicular to the segment.
In other words, if we take a line segment AB and draw a line perpendicular to it at its midpoint M, then that line will cut the segment AB into two equal halves, and will also form right angles with segments AB.
This theorem can be proved using basic geometry concepts such as congruent triangles and the definition of perpendicularity.
Applications of the Perpendicular Bisector Theorem can be seen in a variety of fields, such as architecture, engineering, and cartography. For example, in construction, the perpendicular bisector of a foundation wall can help determine the correct placement of load-bearing walls for a stable structure. In cartography, the Perpendicular Bisector Theorem can be used to construct accurate maps and measure distances between points.
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