Question

DEAR is trapezium in which DE parallel RA and DR=EA.prove that Angle D =angle E

Answer 1

Given : DEAR is an isosceles trapezium 
Construction :FA ║DR and FA = DR
Proof :
as FA ║DR and FA = DR ; DFAR is a parallelogram
∠1+∠2 = 180°____________(1)
 as DR=EA and DR = FA
∴FA =EA
∴ΔFAE is an isosceles triangle
∠3=∠2
∠4+∠3 = 180° (linear pair)________(2)

from (1) and (2) we get 

∠4+∠3=∠1+∠2

∠4=∠1  (as ∠3=∠2)

hence ∠D =∠E

proved ......................

hope it helped :)

Answer 2

hence proved that ang D is egual to ang E