1. Medians and Altitudes
Section 5-4

2. Medians
Median of a triangle: segment whose endpoints are a vertex and the midpoint of the opposite side
A triangle’s three medians are always concurrent.

3. Theorem 5-8 Concurrency of Medians Theorem
The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side.
DC = DJ
EC = EG
FC = FH
Centroid of a triangle: the point of concurrency of the medians; also called the center of gravity; ALWAYS inside the triangle

4. Finding the Length of a Median
If XA = 8, what is the length of XB?
XA = XB
(8) =( x)
12 = x
If ZA = 9, what is the length of ZC?
ZA = ZC
(9) =( x)
13.5 = x

5. Altitudes
Altitude of a triangle: the perpendicular segment from a vertex of a triangle to the line containing the opposite side

6. Example 2 Identifying the Medians and Altitudes
Is each segment a median, an altitude, or neither?
a median
neither
an altitude

7. Concurrency of Altitudes
Concurrency of Altitudes Theorem: the lines that contain the altitudes of a triangle are concurrent
Orthocenter of a triangle: the point of concurrency of the lines that contain the altitudes
The orthocenter can be inside, on, or outside the triangle (like the circumcenter!).

8. Summary
Pg #8-13, 17-20, 24-27
Show work for #8-10

9. Assignment
Pg #8-13, 17-20, 24-27
Show work for #8-10