Abcd Is Trapezium In Which Ab Dc Dc Is Produced To E Such That Ce Ab Prove That Ar В–Іabd Ar В–Іbce

ABCD is a trapezium in which AB || DC. DC is produced to E such that CE= AB, prove that ar(△ABD) = ar (△BCE).


Solution    :-

   Produce BA to M such that DM perpendicular BM and draw BN perpendicular DC.

Now,       ar(△ABD) = 1/2 (AB x DM)               ….(i)

              ar(△BCE) = 1/2 (CE x BN)                …..(ii)

 Since,triangles ABD and BCE are between the same parallels. Therefore,

                       DM = BN                              ………(iii)

Also,                AB = CE    (Given)            …………(iv)

    From (iii) and (iv), we get

           1/2(AB x DM) = 1/2(CE x BN)

  ⇒       ar (△ABD) = ar (△BCE) (Using (i) and (ii))