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Line Bisectors And Angle Bisectors

Perpendicular bisector theorem

Math

Theorem 1

Prove that: Any point on the right bisector of a line segment is equidistant from its end points

Given: CDCD is the right bisector of AB\overline{AB} intersecting it at OO. PP is any point on CDCD.

To Prove: APBP\overline{AP} \cong \overline{BP}, i.e. PP is equidistant from AA and BB.