Use ΔABC to answer the question that follows: Triangle ABC. Point F lies on AB. Point D lies on BC. Point E lies on AC. AD, BE, and CF passes through point G. Line AD passes through point H lying outside of triangle ABC. Line segments BH and CH are dashed

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 Line segment AB Point E is a midpoint of Line segment AC Draw Line segment BE Draw Line segment FC by Construction
Point G is the point of intersection between Line segment BE and Line segment FC Intersecting Lines Postulate
Draw Line segment AG by Construction
Point D is the point of intersection between Line segment AG and Line segment BC Intersecting Lines Postulate
Point H lies on Line segment AG such that Line segment AG ≅ Line segment GH by Construction
I BGCH is a parallelogram Properties of a Parallelogram (opposite sides are parallel)
II Line segment FG is parallel to line segment BH and Line segment GE is parallel to line segment HC Midsegment Theorem
III Line segment BD ≅ Line segment DC Properties of a Parallelogram (diagonals bisect each other)
IV Line segment GC is parallel to line segment BH and Line segment BG is parallel to line segment HC Substitution
Line segment 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?
IV, II, III, I
II, IV, I, III
IV, II, I, III
II, IV, III, I