2020-04-26 05:07:15
In triangle ACE, G is the centroid and BE=9. Find BG and GE. (segments BE and AD cross in the middle of the triangle, BE overlaps AD and C is at the top of the triangle, and A is on the left corner and E is on the right) Thank You So Much!!! ^0^
2020-04-26 06:03:54

For the answer to the question, above BE is a median. Along with any median, the centroid of a triangle is always located 2/3 of the way from the vertex to the midpoint of the opposite side, so the centroid G is 2/3 of the way from E to B.  So we have GE = (2/3)BE.  Furthermore, by segment addition, BG + GE = BE.  Since BE = 9, GE = (2/3)(9) = 6.  Then BG + 6 = 9, which gives BG = 3.  I hope this helps you.