Special Properties of the Centroid

1) Using what you know about medians, construct the centroid in the triangle below. [br]2) Find the length of the segment from point A to the centroid. [br]3) Now find the length of the segment from the centroid to the midpoint of the side OPPOSITE of A. [br]What do you notice?[br]4) Repeat this process for the other 2 medians.
Based on your observations above, what is the ratio of the long piece of the median to the short piece?
Given: Triangle ABC has Centroid labeled G. D is the midpoint of BC, E is the midpoint of AC and F is the midpoint of AB.
If the length of median AD is 12 units long, how long is AG?
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– Michal Grissom

Information: Special Properties of the Centroid