If you have a simple sierpinski's triangle (3 up 1 down).
Does the line intersecting the two midpoints of the triangles "legs" also intersect the mid-point of the height? (if it is a equilateral triangle)
Since the height of the triangle is equal to the height of the opposite triangle, I would say that since the two heights are equal, the midpoint of the "total" height is the line connecting the two leg midpoints (which form the shared side of the two smaller triangles I'm talking about).
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