Sierpinski's Triangle: Does the Line Intersect the Midpoint?

[yyttr2]

easy question :)

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)

 

[Char. Limit]

Hmm...

sort of a guesstimate here, but I think it would.

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).

Tell me if my explanation makes no sense, please.

 

[haushofer]

Doesn't the forum advice you to be "descriptive" in your title? :')