Ninth grade students using a dynamic geometry program are asked to explore possible definitions of median in the triangle formed by the white dots.[br]When the students choose a vertex and ask the program to produce a median, the program responds by drawing the white line and the gold dot (see below).[br][br]Students explore the values of areas, angles and side lengths and suggest the following “definitions” – [br][br][i][b]A – a median divides the side opposite the vertex in two equal pieces[br][br]B – a median divides the area of the triangle into two equal areas[/b][/i][br][br]Can you show that these definitions are equivalent – if either one is true then the other is as well?[br][br]Why might definition A be preferable to definition B ? Why might definition B be preferable to definition A ?[br][br]Can the definition of median be generalized to polygons with more than three sides?