[color=#000000]Recall [/color][color=#ff7700][i]if 2 triangles have equal bases and equal heights, they have equal areas.[br] [/i][/color][br][color=#000000]Since this is so, we can [i]informally[/i] conclude that[/color] [color=#0000ff][b]the 3 medians of any triangle split this triangle up into[/b][/color] [color=#ff7700][b]6 smaller triangles of equal area. [/b][/color][br][br]Feel free to move the triangle's white vertices anywhere you'd like at any time. [br][br][color=#000000]Again, this applet displays an [/color][i]informal illustration[/i][color=#000000] of this fact using transformational geometry techniques. [br][/color][i][color=#ff00ff][br]Yet how could you formally prove what this applet informally illustrates? [/color][/i]