#### Answer

$D$

#### Work Step by Step

Option A is true. Plane ABCD is parallel to plane EFGH. Therefore, this answer is incorrect because we are looking for the false statement.
Option B is true. Plane ABCD and plane CDHG both intersect line CD. Therefore, this answer is incorrect because we are looking for the false statement.
Option C is true. Plane ABCD and plane ABC are indeed the same plane. Therefore, this answer is incorrect because we are looking for the false statement.
Option D is false. Plane ADHE and plane DCG are not parallel; in fact, they are perpendicular to one another. Therefore, this answer is correct because it is a false statement, which is what we are looking for.