A line
\(l\) is the perpendicular bisector of a line segment
\(
AB\). If a point
\(P\) lies on line
\(
l\), prove that the distances from
\(
P\) to
\(A\) and
\(B\) are equal.
Proof:
Consider \(∆ PCA\) and \(∆ PCB\).
\(AC = BC\) (\(C\) is the mid-point of \(AB\))
\(∠ PCA = ∠ PCB =\) \(^°\) (Given)
\(PC = PC\) (Common)
So, by rule, \(∆ PCA ≅ ∆ PCB\)
And so, \(PA = PB\) [By CPCT]
Hence, we proved.