Question

Question 15
Two lines I 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 I and m. Prove that n is the bisector of the angle formed by I and m.

Answer 1

In $\Delta OQPand\Delta ORP,$
$\angle PQO=\angle PRO={90}^{\circ }$
[since, P in equidistant from I and m, so PQ and PR should be perpendicular to lines I and m respectively]
OP = OP [comon side]
$\therefore \Delta OQP\cong \Delta ORP$ [by RHS congruence rule]
$\Rightarrow \angle POQ=\angle POR$ [by CPCT]
Hence, n is the bisector of $\angle QOR.$