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).
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))