A median of a triangle is a line segment joining a vertex of a triangle to the midpoint of the opposite side. The three medians of a triangle are drawn below.
[asy] pair A,B,C,X,Y,Z; A = (0,0); B = (1,0); C = (0.3,0.8); X = (B+C)/2; Y = (A+C)/2; Z = (A+B)/2; draw(A--X, red); draw(B--Y,red); draw(C--Z,red); draw(A--B--C--A); [/asy]
Note that the three medians appear to intersect at the same point! Let's try this out with a particular triangle. Consider the triangle with , , and .
(a) Let be the midpoints of respectively. Find the equations of medians and
(b) Show that the three medians in part (a) all pass through the same point.