In the figure , ABCD is a parallelogram . AE=BF and C is parallel to FH . Prove that

(1) EFCD is a parallelogram

(2) GHFC is a parallelogram

(3) parallelogram GHFC and ABCD are equal in area

My work :

(1) BC // AD , AE=BF , AD=BC

(corresponding angle)

No. You mean congruent to

DE// CF , AF// DC

Hence , EFCD is a paralleogram.

Apart from that this is fine.
(2) DH // CF , CG//HF

Hence , GHFC is a parallelogram .

OK.
(3) not really sure .

Use the result from your previous post: parallelograms on the same base and between the same parallels are equal in area. Look first at **CF**DE and **CF**GH; then at **CD**EF and **CD**AB. (Note the bold type.)