The perpendicular bisector b of a line segment AB is a line which is perpendicular to the line segment and passes from the middle of it.
We can see that the distance of any point of the perpendicular bisector is equal from the two endpoints of the line segment. AC = BC.
The proof is simple. We compare the two triangles ADC and BDC.
The equality of the distances AC and BC is used in many other proofs in euclidean geometry.
The reverse is also true.
Any point which has equal distances from the two endpoints of a line segment is on the perpendicular bisector of it.
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