1. Geometry 5-3 Medians and Altitudes A median of a triangle: a segment from the midpoint of a side to the opposite angle. Centroid: where all 3 medians intersect

2. Finding the Centroid The centroid splits a median into 1/3 and 2/3 parts A B C X Y Z P 30 ÷ 3 = 10 AP = 20 XP = 10 If AX = 30 12 ÷ 2 = 6 PZ = 6 CZ = 12 + 6 = 18 If CP = 12 PB = 18 BY = 27 If YP = 9

3. Examples Segment AE is a median for ΔABC. If BE = 3x – 5 and CE = x + 1, what is the length of BC? A B C E BE = CE 3x – 5 = x + 1 -x -x 2x – 5 = 1 +5 +5 2x = 6 x = 3 BE = 3(3) – 5 = 4 BC = 8

4. 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 = (1/2)bh Orthocenter: where the 3 altitudes intersect

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