Marden's theorem

Imagine we have a triangle with sides labeled A, B, and C. We draw a line that goes from the midpoint of side A to the opposite corner of the triangle. Let's call that corner D.

Marden's Theorem tells us that if we draw two more lines, one from the midpoint of side B to corner D and one from the midpoint of side C to corner D, those two lines will intersect on the line we drew from the midpoint of side A.

It's like if you were standing at one end of a building and your friend was standing at the other end. You both draw a line towards each other, and where those lines intersect is the middle of the building.

Marden's Theorem is useful in a lot of math problems involving triangles, especially when we need to find the location of the intersection point or how to draw geometric shapes.