Perpendicular bisector

A perpendicular bisector of a triangle is a straight line passing through the midpoint of a side and being perpendicular to it. That means it is forming a right angle with it.

There are 3 perpendicular bisectors for a triangle. These 3 meet in a single point which is called the circum centre of a triangle. Thales's theorem implies that if the circum centre is located on one side of the triangle, then the opposite angle is a right one. If the circum centre is located inside the triangle, then the triangle is acute and if it is located outside the triangle, then the triangle is obtuse.

Altitude of a triangle

Altitude of a triangle is a straight line passing through a vertex and perpendicular to the opposite side. This opposite side is called the base of the altitude and the point where the altitude intersects the base is called the foot of the altitude.

The three altitudes of a triangle intersect in a single point called the orthocentre of the triangle. The orthocentre lies inside the triangle if and only if the triangle is acute.

Angle bisector

An angle bisector of a triangle is a straight line through a vertex which cuts the corresponding angle in half. The three angle bisectors intersect in a single point called the incentre of a triangle. Incentre is the centre of the triangle's incircle.

The incircle is the circle which lies inside the triangle and touches all the three sides.

This is all about bisectors of a triangle.