In parallelogram ABCD, point E is the midpoint of side AB. It is known that EC = ED.

In parallelogram ABCD, point E is the midpoint of side AB. It is known that EC = ED. Prove that the given parallelogram is a rectangle.

Consider triangles AED and EBC. From the condition AE = EB, EC = ED, and, like a parallelogram, AD = BC. So the triangles are equal. Therefore, the angle EAD is equal to the angle EBC.
Considering that the sum of the angles of a parallelogram adjacent to one side is 180 degrees (by the property of parallel lines), each of these angles is 90 degrees. The opposite angles are also 90 degrees (since the opposite angles in the parallelogram are equal).
Therefore, a parallelogram is a rectangle.