Use ΔABC to answer the question that follows:
Given: ΔABC
Prove: The three medians of ΔABC intersect at a common point.
When written in the correct order, the two-column proof below describes the statements and justifications for proving the three medians of a triangle all intersect in one point:
Statements Justifications
Point F is a midpoint of Point E is a midpoint of Draw Draw by Construction
Point G is the point of intersection between BE and FC Intersecting Lines Postulate
Draw AG by Construction
Point D is the point of intersection between AG and BC Intersecting Lines Postulate
Point H lies on AG such that AG≅GH by Construction
I BGCH is a parallelogram Properties of a Parallelogram (opposite sides are parallel)
II BD≅DC Properties of a Parallelogram (diagonals bisect each other)
III GC||BH and BG||HC Substitution
IV FG||BH and GE||HC Midsegment Theorem
AD is a median Definition of a Median
Which is the most logical order of statements and justifications I, II, III, and IV to complete the proof?
III, IV, II, I
IV, III, I, II
III, IV, I, II
IV, III, II, I