Download
1 / 7
70 likes | 222 Views
5.3 Medians & Altitudes of a . Pg 279. 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. Centroid.
E N D
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
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
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
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. _ _
Orthocenter • Orthocenter- the lines containing the three altitudes of a triangle are concurrent, pt of concurrency is the orthocenter orthocenter
