To solve this problem, we use 2 facts:
1. In a parallelogram ABCD, the 2 diagonals, AC and BD, bisect each other.
2. In a circle, the angle subtended by the diameter at the circumference is a right angle.
Label the crossing of 2 diagonals, AC and BD, O. From 1. and the given condition: AC=BD,
OA=OB=OC=OD=R
Thus, point O is the center of a circle with radius R that circumscribes parallelogram ABCD.
And AC and BD are the diameters of circle O. From 2, ∠A=∠B=∠C=∠D=90°
Therefore, parallelogram ABCD is a rectangle, and AD is perpendicular to DC. Q.E.D.