AD is parallel to BC, BD is perpendicular to AD, so BD is perpendicular to BC, triangle ADB and triangle BDC are right triangles, and E and F are midpoint, so DE= semi-AB, DC= semi-CD, and DE=BF, so AB=∠A=C, which proves that triangle DEB and triangle Bd F are congruent, so DF is parallel to BE, so abcd is parallelogram, so ∞.