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