The steps shown can be used to prove that the medians of a triangle meet at a point.
Triangle A B C is shown on an x and y-axis. Lines are drawn from each point to the opposite side and intersect at point G. Point A is at (0, 0), point D is at (c, 0), point C is at (2 c, 0), point B is at (2 a, 2 b), and point E is at (a, b).
1. Define segments BD and CE as medians of triangle ABC.
2. Write linear equations for Line B D and Line C E.
3. Use a system of linear equations to solve for the coordinates of intersection point G.
4. Write the equation of Line A G.
5. Write an expression for the midpoint of BC, point F.
6. ?
Write a linear equation for each side of the triangle.
Write an expression for the midpoint of AC and BC.
Show that A F is congruent to BD and CE.
Show that A F is the median of BC.