Perpendicular bisector - Math.net
https://www.math.net/perpendicular-bisector
WEBThe Perpendicular Bisector Theorem states that any point on the perpendicular bisector is equidistant from the segment's endpoints. Let T be on the perpendicular bisector, RS, below. Since RS is perpendicular to PQ, PST and QST are both right triangles. Since PS = SQ, PST≅ QST by the Side-Angle-Side Theorem.
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