Question

AB is a line segment . P and Q are points on opposite sides of AB such that each of them is equidistant from the points A and B . Show that the line PQ is the perpendicular bisector of AB .

Answer 1

ANSWER:

• SEE ATTACHMENT

E XPLANATION:

• 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)

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.

then triangle aop congruent to triangles bop.hence proved that op is that bisector and parpendicular of AB.

• Hence proved