5-3 VOCABULARY Median of a triangle Centroid of a triangle Altitude of a triangle Orthocenter of a triangle

5-3 Medians & Altitudes of ’s Geometry

Median of a triangle Seg AM is a median of  ABC A B M C Median of a triangle- segment whose endpts are a vertex of a triangle and the midpt of the opposite side. The three medians of a triangle are ALWAYS concurrent! B M C

Centroid Centroid- the pt of concurrency of the 3 medians of a triangle (i.e. pt. X) The centroid is always inside the triangle The centroid is also the balancing point of the triangle. A M O X C N B

Centroid Thm 5-3-1 Concurrency of Medians of a  The medians of a triangle intersect at a pt that is 2/3 of the distance from each vertex to the midpt of the opposite side. (i.e. AX=2/3 AN) Example 1: If MX=4, find MB and XB BX=2/3 MB  MX=1/3 MB ___ = ___ = MB XB = ____ B O N X C A M

Example 2 Find the coordinates of the centroid of the triangle with vertices L(3,6) K(5,2) J(7,10). (Hint: graph it 1st!) Then, find midpoints and draw medians. Identify centroid. (5,6)

Ex. 2

Altitude of a triangle _ _ Altitude of a triangle- the  seg from a vertex to the opposite side of the line that contains the opposite side. _ _

Orthocenter orthocenter Orthocenter- the lines containing the three altitudes of a triangle are concurrent, pt of concurrency is the orthocenter orthocenter

Ex. 3 Find the orthocenter of with vertices X(-4,-9), Y(-4,6), & Z(5,-3).

Ex. 3

Assignment