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Three segments are drawn from opposite corners of a hexagon

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Three segments are drawn from opposite corners of a hexagon

by airan » Mon Jul 14, 2008 9:12 am
Three segments are drawn from opposite corners of a hexagon to form six triangles.These segments all bisect each other at point A. Are all of the triangles equilateral?

1. all six sides of hexagon are the same length
2. the three segments drawn between the opposite corners are equal length.
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by tzink » Mon Jul 14, 2008 1:45 pm
(1) and (2), in different ways, both state that the polygon is a regular hexagon. If this is the case, then the interior angles add up to 180(n-2), or 720. 720/6 = 120. each of these angles is bisected by a segment (the segments that form the 6 triangles), so each of those angles is 60 deg.

Now, the angles that are formed by the intersection of the triangle-forming segments must add up to 360 (because they go all the way around the circle/hexagon). 360/6 = 60

So, we know that all three angles of each triangle are 60 deg, which makes them equilateral. Both are SUFFICIENT

Answer is D.
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