Question 1143287
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ABCDEF is a regular hexagon, so all the side lengths are the same.<br>
The interior angles of a regular hexagon are each 120 degrees.<br>
Triangles ABC and DEF are isosceles, because all the side lengths of the hexagon are congruent.<br>
Angles B and E are each 120 degrees; that makes angles BAC, BCA, EDF, and EFD each 30 degrees.<br>
And that makes angles ACD, CDF, DFA, and FAC all right angles.<br>
And that makes ACDF a rectangle.<br>
Note your statement of the problem says to show that ADCF is a rectangle; it is not....