This applet can be used to see the properties of parallelograms by symmetry. Drag any of the blue points to change the parallelorgam. Click the show button to create a copy of the prallelorgam. Drag the orange point to rotate the copy around the center of the parallelogram.
Construct a general parallelogram.Click on the Show button and rotate the second parallelogram on 180 degrees around the intersection point of the diagonals. Use this symmetry to notice the three properties: the opposite sides are congruent, the opposite angles are congruent and its diagonals bisect each other. Click on the Hide button and drag the blue points to make a rectangle. Click the Show button to show a copy of the rectangle. Rotate the rectangle on 180 degrees around the intersection of the diagonas. Use this symmetry to notice the three propertiesof the parallelograms. Notice an additional property of the diagonals - they are congruent.