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 Line segment BD ≅ Line segment DC Properties of a Parallelogram (diagonals bisect each other) 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 GC is parallel to line segment BH and Line segment BG is parallel to line segment HC Substitution IV BGCH is a parallelogram Properties of a Parallelogram (opposite sides are parallel) 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? II, III, I, IV III, II, I, IV II, III, IV, I III, II, IV, I
