Answers

2015-10-23T18:47:18+05:30
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

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⇒ Therefore , it is proved that AB  | | ED

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