Question 999029: Given that polygon ABCDEF is a regular hexagon, prove that AC is congruent to AE
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
Draw the diagonal AC and AE in the polygon.
Consider two triangles: ABC and AEF.
They are isosceles triangles, since the sides of ABCDEF are congruent.
In addition, these triangles have congruent angles B and F (they are congruent as interior angles of the regular hexagon).
According to SAS-criterion for the congruency of triangles, the triangles are congruent.
Hence, their corresponding sides are congruent: AC = AE.
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