Question

P is a point equidistant from two lines l and m intersecting at point A. Show that the line AP bisects the angle between them.

Answer 1

$\text{Given that lines l and m intersect each other at A. Let PB}\perp l,$
$PC\perp m.\text{It is given that}PB=PC.$
To show that $\angle PAB=\angle PAC$
let us consider $△$ PAB and $△$ PAC.
$PB=PC\text{(Given)}$
$\angle PBA=\angle PCA={90}^{\circ }\text{(Given)}$
$PA=PA$ (Common)
$\text{So,}△PAB\cong △PAC\text{(RHS rule)}$
$\text{So,}\angle PAB=\angle PAC\text{(c.p.c.t.)}$