Angle bisectors and medians

Math

Definition

An angle bisector is a ray that divides an angle into two equal parts. A median is a segment from a vertex of a triangle to the midpoint of the opposite side. The three angle bisectors meet at the incenter, and the three medians meet at the centroid.

Examples

  • The three medians of a triangle always intersect at the centroid, which is the triangle's balance point located 2/3 of the way from each vertex
  • The incenter (where angle bisectors meet) is equidistant from all three sides and is the center of the inscribed circle
Key Fact

Centroid divides each median in a 2:1 ratio from vertex to midpoint

Related Terms

Triangles Isosceles triangle theorem Two-column proofs Measuring angles

Study This Concept

Practice angle bisectors and medians with free review games in these units:

Geometry Unit 5: Triangle Relationships