1. The intersection of the medians is called the CENTROID. How many medians does a triangle have?

2. Theorem 5.8 The length of the segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint.

3. A B F X E C D

4. A B F X E C D

5. In  ABC, AN, BP, and CM are medians. A B M P E C N If EM = 3, find EC. EC = 2(3) Ex: 1 EC = 6

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

7. In  ABC, AN, BP, and CM are medians. A B M P E C N If CM = 3x + 6, and CE = x + 12, what is x? CM = CE + EM Ex: 3 x = 8 3x + 6 = (x + 12) +.5(x + 12) 3x + 6 = x + 12 +.5x + 6 3x + 6 = 1.5x + 18 1.5x = 12

8. Altitude

9. The intersection of the altitudes is called the ORTHOCENTER. How many altitudes does a triangle have?

10. Tell whether each red segment is an altitude of the triangle. The altitude is the “true height” of the triangle.