Vector techniques can be used to prove and derive many geometric relationships.

Vector techniques can be used to prove and derive many geometric relationships. Use the following theorem from Euclidean geometry as you complete this assessment: Theorem: A triangle and its medial triangle have the same centroid.Scenario: The medial triangle of a triangle ABC is the triangle whose vertices 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 34 sentences) that the theorem is true.