5-4 Medians and Altitudes
Objective
To identify properties of medians and altitudes of a triangle
Dynamic Activity
Medians and Altitudes
Lesson Vocabulary
- median of a triangle
- centroid of a triangle
- altitude of a triangle
- orthocenter of a triangle
In the Solve It, the last set of segments you drew are the triangle's medians. A median of a triangle is a segment whose endpoints are a vertex and the midpoint of the opposite side.
Essential Understanding A triangle's three medians are always concurrent.
Take Note Theorem 5-8: Concurrency of Medians Theorem
The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side.
You will prove Theorem 5-8 in Lesson 6-9.
In a triangle, the point of concurrency of the medians is the centroid of the triangle. The point is also called the center of gravity of a triangle because it is the point where a triangular shape will balance. For any triangle, the centroid is always inside the triangle.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs