5-3 M EDIANS AND A LTITUDES OF A T RIANGLE  Use the properties of Medians of a triangle  Use the properties of Altitude of a triangle

D EFINITIONS 1. A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. 2. The point of concurrency point is called the Centroid. 3. The centroid is always inside the triangle.

S PECIAL P ROPERTY OF C ENTROID :  The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side

I NTERESTING P ROPERTY OF A C ENTROID  The centroid is the balancing point of a triangular model of uniform thickness and density.

D EFINITIONS 1. An Altitude of a triangle is the perpendicular segment from a vertex to the opposite side or the line than contains the opposite side (height of the triangle). 2. The orthocenter is the point of concurrency of the altitudes.

An Altitude and its orthocenter can lie inside, on, or outside the triangle.

Remember the Distance and Midpoint formulas: Write them below: Distance Formula: Midpoint Formula: