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Equilateral Triangles: Horizontal = Slant

Question

Assume we have an equilateral triangle oriented to where one of its base is perpendicular to a vertical line. Pick a point on one of the edges and draw a parallel line to the base from edge to edge; while also measuring from the point to the top most vertex of the triangle.  How often are the two line segments the same length?

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They should always be the same length.

 You understood the question perfectly.  I guess this one was too easy :P

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