1. Warm-Up Find the area of each triangle. 5 20 12.5 8

2. Geometry 5-3 Medians and Altitudes

3. Median A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.

4. Centroid The centroid of a triangle is where all three medians of the triangle intersect. The centroid is also known as the center of gravity because it is the point where a triangular region would balance.

5. Finding the Centroid The centroid is always found at 2/3 the length of the median (closer to the side than the vertex) A B C X Y Z P AP = 2/3AX BP = 2/3BY CP = 2/3CZ XP = 1/3AX YP = 1/3BY ZP = 1/3CZ AlsoCentroid

6. Examples In ∆LMN, RL = 21 and SQ =4. Find LS and NQ.

7. Altitude An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side. The altitude of a triangle is the height you would use for the area of a triangle: A =.5bh

8. Orthocenter The orthocenter of a triangle is where all three altitudes meet. orthocenter