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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.

 Mar 8, 2021
edited by Guest  Mar 8, 2021
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Pro-tip: The point is the centroid of the triangle!

 Mar 8, 2021

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