5.3 Medians & Altitudes of a 

1. 5.3 Medians & Altitudes of a  Pg 279

2. Median of a triangle Seg AM is a median of  ABC A • 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

3. 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

4. Thm 5.7Concurrency 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: If MX=4, find MB and XB • XB=2/3 MB  XM=1/3 MB • So, MB=12 and XB=8 A M O X C N B

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

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

7. Assignment