Since quadrilateral MATH has opposite sides congruent and parallel, it is a parallelogram.
In a parallelogram, opposite sides are parallel and congruent, but the opposite angles are also congruent.
Therefore, we can say that angle M is congruent to angle H, and angle A is congruent to angle T.
Option A states that MT is congruent to AH, which is not always true for a parallelogram.
Option B states that MT is perpendicular to AH, which is also not always true for a parallelogram.
Option C states that angle MHT is congruent to angle ATH. Since angle M is congruent to angle H and angle A is congruent to angle T, we can say that angle MHT is congruent to angle ATH. This is always true for a parallelogram, as opposite angles are congruent.
Option D states that angle MAT is congruent to angle MHT. This is not always true for a parallelogram. While angle MHT is congruent to angle ATH (as explained in Option C), there is no reason to assume that angle MAT is congruent to angle MHT.
Therefore, the correct answer is: C. Angle MHT is congruent to Angle ATH.