1. 5-3 VOCABULARY Median of a triangle Centroid of a triangle
Altitude of a triangle
Orthocenter of a triangle

2. 5-3 Medians & Altitudes of ’s
Geometry

3. 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

4. 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

5. 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

6. 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)

7. Ex. 2

8. 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. _ _

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

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

11. Ex. 3

12. Assignment