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.

Guest Mar 8, 2021

edited by
Guest
Mar 8, 2021