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Equidistant

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Equidistant means "at the same distance."

Thus, for instance, if triangle $\triangle ABC$ is isosceles with base $BC$ , points $B$ and $C$ are equidistant from point $A$ .

Similarly, the perpendicular bisector of a line segment is the set of points equidistant from the endpoints. So, given segment $\overline{AB}$ and a point $C$ such that $AC = BC$ , we know (by definition) that $C$ is on the perpendicular bisector of $\overline{AB}$ . Also, given $C$ on the perpendicular bisector of $\overline{AB}$ , we know that $AC = BC$ .

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