Question

ab is a line segment p and q are point on opposite sides of ab such that each of them is equidistant from the point a and b. show that line pq is perpendicular bisector of ab

Answer 1

in figure ab is a straight line on which pb and ap sides are standing.
So,
in triangle aop and bop
op is a bisector of angle apb and ab line.
then, angle apo=bpo (op is the bisector of angle apb)
ao =ob (op is perpendicular and bisector of ab)
and, angle aop =bop=90 degree (op perpendicular ab making right angle )
Or,op =op (common )
then triangle aop congruent to triangles bop.
hence proved that op is that bisector and parpendicular of AB.
hence proved....

hoped helps..

Answer 2

hope it helps.... .........
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