1. 5.3 CONCURRENT LINES, MEDIANS AND ALTITUDES PART B LEQ: How do we construct and use medians and altitudes?

2.  Median of a triangle: a segment whose endpoints are a vertex and the midpoint of the opposite side  Altitude of a triangle: the perpendicular segment from a vertex to the line containing the opposite side

3. Theorem 5-8 The medians of a triangle are concurrent (intersect) at a point that is two thirds the distance from each vertex to the midpoint of the opposite side. DC = 2/3DJ EC = 2/3EG FC = 2/3FH The point of intersection is called the centroid. D G F H E C J Centroid

4. Example C is the centroid. 1.) If CJ = 12, find DC and DJ. DC=2/3 (DJ) and CJ=1/3 (DJ) 2.) If FC = 15, find CH and FH. 3. If GE = 30, find GC and CE. D G F H E C J

5. Bubble sheet Centroid: Medians (vertex to midpoint) 2:3/1:3 rule Pieces of median are a 2:1 ratio

6. Example Is ST a median, an altitude or neither? What is UW? What is VX? What is CA? W S V T U C A X

7.  The point of concurrency of the altitudes is called the orthocenter.  The point of concurrency of the medians is called the centroid.

8. Orthocenter: Altitudes/height (vertex to opposite side & makes right angle) May be inside of, outside of, or on triangle

9. Let’s practice: Identify each point of concurrency below: ab d c