If perpendiculars from any point with an angle on its arms are congruent, prove that it lies on the bisector of that angle.

In perpendiculars from any point within an angle on its arms are congruent,prove that it lies on the bisector of that angle.

Two right angles are congruent

Two acute angles are congruent

Congruent angles

The point of intersection of the angle bisectors of a triangle is :

Prove that, angles inscribed in the same are arc congruent.

In any triangle ABC,if the angle bisector of /_A and perpendicular bisector of BC intersect, prove that they intersect on the circumcircle of the triangle ABC

Line l is the bisector of an angleA and B is any point on I. BP and BQ are perpendiculars from B to the arms of angleA (see figure). Show that: BP=BQ or B is equidistant from the arms of angleA .

Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.