Math
Angle bisectors and medians.
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
Real-world.
- 1 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
- 2 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