Theorem: A triangle and its medial triangle have the same centroid.
Scenario:
The medial triangle of a triangle ABC has vertices that are located at the midpoints of the sides AB, AC, and BC of triangle ABC. From an arbitrary point O that is not a vertex of triangle ABC, you may take it as a given fact that the location of the centroid of triangle ABC is the vector (vector OA + vector OB + vector OC)/3.
Task:
A. Use vector techniques to prove that a triangle and its medial triangle have the same centroid, stating each step of the proof.
1. Provide written justification for each step of your proof.
B. Provide a convincing argument short of a proof (suggested length of 3-4 sentences) that the theorem is true.