1. Medians
Median
vertex to midpoint

2. Example 1 M D P C N What is NC if NP = 18? MC bisects NP…so 18/2 9
If DP = 7.5, find MP. 15 =

3. Three – one from each vertex
How many medians does a triangle have?
Three – one from each vertex

4. They meet in a single point.
The medians of a triangle are concurrent.
The intersection of the medians is called the CENTRIOD.
They meet in a single point.

5. Theorem
The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint. 2x x

6. In ABC, AN, BP, and CM are medians.
Example 2
In ABC, AN, BP, and CM are medians.
If EM = 3, find EC. C
EC = 2(3) N P E
EC = 6 B M A

7. In ABC, AN, BP, and CM are medians.
Example 3
In ABC, AN, BP, and CM are medians.
If EN = 12, find AN. C
AE = 2(12)=24
AN = AE + EN N P
AN = E B
AN = 36 M A

8. In ABC, AN, BP, and CM are medians.
Example 4
In ABC, AN, BP, and CM are medians.
If EM = 3x + 4 and CE = 8x, what is x? A B M P E C N
x = 4

9. In ABC, AN, BP, and CM are medians.
Example 5
In ABC, AN, BP, and CM are medians.
If CM = 24 what is CE? A B M P E C N
CE = 2/3CM
CE = 2/3(24)
CE = 16

10. vertex to opposite side and perpendicular
Altitude
Altitude
vertex to opposite side and perpendicular

11. The altitude is the “true height” of the triangle.
Tell whether each red segment is an altitude of the triangle.
The altitude is the “true height” of the triangle.
YES NO
YES

12. Three How many altitudes does a triangle have?
The altitudes of a triangle are concurrent.
The intersection of the altitudes is called the ORTHOCENTER.

13. Tell if the red segment is an altitude, perpendicular bisector, both, or neither?
PER. BISECTOR
BOTH