In the parallelogram ABCD, point E is the middle of the CD side. It is known that EA = EB.

In the parallelogram ABCD, point E is the middle of the CD side. It is known that EA = EB. Prove that the data is a rectangular parallelogram.

The opposite sides of the parallelogram are equal, that is, AD = BC. Consider triangles AED and EBC, in which ED equals EC, AE equals EB and AD equals BC, hence the triangles are equal on three sides, which means that the angle ADE = the angle ECB.

Recall also that the opposite angles of the parallelogram are equal, therefore: angle DAB = angle ABC = angle BCD = angle CDA

The sum of the angles of a parallelogram 360 °: Angle DAB = Angle ABC = Angle BCD = Angle CDA = 360 °: 4 = 90 °

All angles of a parallelogram are straight, and therefore this parallelogram is a rectangle.