Step 1 :Given that $E F G H$ is a parallelogram and angle HEF is right.
Step 2 :In a parallelogram, opposite sides are parallel.
Step 3 :If we consider the line segment EF as a transversal line, then angle HEF and angle FGH are alternate interior angles.
Step 4 :According to the properties of parallel lines, alternate interior angles are congruent when parallel lines are cut by a transversal.
Step 5 :Therefore, if angle HEF is a right angle, then angle FGH should also be a right angle.
Step 6 :Final Answer: \(\boxed{\text{A) Alternate interior angles are congruent when parallel lines are cut by a transversal.}}\)