Viviani Theorem

One of the well know theorem about equilateral triangle is the Viviani's Theorem. It states that given an equilateral triangle and any random point inside. Then sum of the distance of the perpendiculars drawn from this point on the three sides is equal to the length of the altitude of the triangle. Here are some snapshots of the theorem using KSEG. The proof of the theorem is real simple. From E if we draw join the vertices of the original triangle we get three triangles. The area of these is 1/2 base * altitude. Let the  sides be a unit each (recall its an equilateral triangle) then we have
1/2*a*EG+1/2*a*EH+1/2*a*EF=1/2*a*AI
EG+EH+EF=AL
Q.E.D