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Question

In given figure AB is a line-segment. P and Q are points on either side 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
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Solution

Given AB is a line segment .P and Q are two-point on either side of AB such That AP=BPandAQ=BQ

In ΔPAQand ΔPBQ

AP=BP (Given )

AQ=BQ (Given )

PQ=PQ (Common side)

ΔPAQΔPBQ

APQ=BPQ

In ΔPAC and PBC

AP=BP (Given )

APC=BPC We proved above APQ=BPQ

PC=PC (Common Side)

ΔPACPBC

AC=BC....................................(1)

ACP=BCP

ACP+BCP=1800

2ACP=1800

ACP=900.....................(2)

From (1) and (2) the line PQ is the perpendicular bisector of AB. [henceproved]

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