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: StatementsJustifications 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 FCby Construction Point G is the point of intersection between Line segment BE and Line segment FCIntersecting Lines Postulate Draw Line segment AGby Construction Point D is the point of intersection between Line segment AG and Line segment BCIntersecting Lines Postulate Point H lies on Line segment AG such that Line segment AG ≅ Line segment GHby Construction IBGCH is a parallelogramProperties of a Parallelogram (opposite sides are parallel) IILine segment BD ≅ Line segment DCProperties of a Parallelogram (diagonals bisect each other) IIILine segment GC is parallel to line segment BH and Line segment BG is parallel to line segment HCSubstitution IVLine segment FG is parallel to line segment BH and Line segment GE is parallel to line segment HCMidsegment Theorem Line segment AD is a medianDefinition 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
