 M EDIAN : A segment that joins a vertex of the triangle at the midpoint of the side opposite that vertex.  The median splits the side into two equal parts

 Example 1  In EFG, FN is a median.  Find EN if EG = 11. ▪ If FN is a median, then N is a midpoint of EG ▪ If EG = 11, then EN is (left) half ▪ EN = ½  11 = 5.5 F E G N

YY OUR T URN IIn  MNP, MC and ND are medians. WWhat is NC if NP = 18? ▪9▪9 IIf DP = 7.5, find MP. ▪1▪15 IIf PD = 7x – 1, CP = 5x – 4, and DM = 6x + 9, find NC. ▪4▪46

 C ENTROID : The point where all three medians of a triangle intersect.  C ONCURRENT : When three or more lines or segments meet at the same point.  X is the centroid of JKM.  QM, JR, and PK are concurrent.

 There is a unique relationship between the length of a segment from the centroid to the vertex and from the centroid to the midpoint.  See the examples below.

 T HEOREM 6-1: The length of a segment from the vertex to the centroid is twice the length of the segment from the centroid to the midpoint.  Note this means: ▪ Centroid to midpoint = 1/3 of whole median ▪ Centroid to vertex = 2/3 of whole median

 Example 2  In XYZ, XP, ZN, and YM are medians.  Find ZQ if QN = 5. ▪ ZQ is centroid to vertex ▪ It’s twice as long as centroid to midpoint ▪ ZQ = 2  5 = 10  If XP = 10.5, what is QP? ▪ QP is centroid to midpoint ▪ It’s half the length of centroid to vertex (no good) ▪ It’s 1 / 3 rd the entire length of the median ▪ QP = 1 / 3  10.5 = 3.5

YY OUR T URN IIn  ABC, AE, BF and CD are medians. IIf CG = 14, what is DG? ▪7▪7 FFind BF if GF = 6.8? ▪2▪20.4

 Assignment  Worksheet #6-1