GIVEN ;-
⇒ ABCDEF is a regular Hexagon
CONSTRUCTION ;-
⇒ Join EA and BD
TO PROVE ;-
⇒ AB | | ED
PROOF ;-
⇒ Now let us take the shape -
⇒ DBCD
⇒ DEFA
In DBCD and DEFA,
⇒ ∠ EFA = ∠ BCD
⇒ CD = EF (They are the sides of the regular hexagon)
⇒ AF = BC (They are the sides of the regular hexagon)
So by , SAS congruence rule -
⇒ Δ EFA ≅ ΔBCD { SAS rule }
⇒ AE = BD { C. P. C . T }
Also AB = ED because they are the sides of the regular Hexagon
--------------------------------------------------------------------------------------
⇒ Therefore , it is proved that AB | | ED
--------------------------------------------------------------------------------------
