In the figure below,ABCDEF is a regular hexagon.prove that ABDE is a rectangle

// hope you can draw the figure//

In Triangles, AFE and BCD,
AF = BC (sides of regular hexagon are equal)
angle AFE = angle BCD (angles of regular hexagon are equal)
EF = DC (sides of regular hexagon are equal)
so, triangle AFE congruent triangle BCD
so, AE = BD (CPCT)

again, AB = DE (sides of regular hexagon are equal)
so, ABDE is a parallelogram

Now, in triangle AFE,
angle AFE + FAE + FEA = 180 (angle sum property of triangle)
or 120 + 2 angle FAE = 180 [all angles of regular hexagon = 120 and FAE = FEA as AF = FE]
or 2 angle FAE = 180 - 120 = 60
or angle FAE = 60 / 2 = 30

so, angle BAE = angle BAF - FAE
= 120 - 30 = 90

so ABDE is a rectangle (proved)