Two lines l and m intersect at the point O and P is a point on a line n passing through the point O such that P is equidistant from l and m. Prove that n is the bisector of the angle formed by l and m.
Given: l and m intersect at point O and P is a point on a line n passing through O and
PQ = PR
To prove: QOP = ROP
Proof: In POR and POQ
PQ = PR (Given)
PQO = PRO = 90° (P is equidistant from l and m)
So PQ and PR should be perpendicular to lines l and m respectively
POR POQ (by RHS congruence)
ROP = QOP (by CPCT)
Hence Proved.