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Sagot :
we have that
If ST is the perpendicular bisector of XY
then
xz=zy
sz is a common side triangle xsz and yzs
xs=ys -----> by applying Pythaorean Theorem in a righ triangle
that means
triangle xsz is congruent with triangle ysz
therefore
ST is the perpendicular bisector of segment XY

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