What does an angle bisector do?

An angle bisector is a line or segment that divides an angle into two smaller angles that are congruent, meaning they have the same measure. This property makes the angle bisector a crucial concept in geometry, especially in the context of triangles. For instance, in a triangle, if one of the angles is bisected, the resulting two angles will each equal exactly half of the measure of the original angle. This is useful in many geometric proofs and constructions, such as finding the incenter of a triangle, which is the point where all the angle bisectors intersect and is also the center of the circle inscribed within the triangle.

The other options represent different concepts in geometry. Connecting midpoints deals with a specific line segment known as a midsegment, forming a right angle pertains to the property of altitudes, and dividing a triangle into equal areas involves additional geometric calculations or constructions, none of which describe the function of an angle bisector.