Let any point on the base BC be d and both sides of the triangle be AB AC.

Link advertising. DE⊥AB DF⊥AC above D.

△ABD = 1/2*DE*AB area

△ area of △ADC = 1/2*DF*AC

Because AB=AC

So the area of △ABC = △ Abd+△ ADC =1/2 * (de+df) * ab.

And because △ ABC =1/2 * (the height on the side of AB) * the area of AB.

So the height on the side of AB =DE+DF.

So the sum of the distances from any point at the bottom to two waists is equal to the height of one waist.