Given that quadrilateral ABDC is a parallelogram; therefore, and .

1. Construct squares on each of the sides of parallelogram ABDC.
2. Construct the diagonals of these squares
3. We know that and . We also know that the diagonals of the squares bisect the vertices, so.
4. Since all have a side congruent to and a side congruent to and an angle between them that is the sum of two 45 degree angles and one of the angles of the parallelogram ABDC the four triangles are congruent by SAS.
5. By CPCTC . Therefore the quadrilateral is a parallelogram that is either a square or a rhombus. Since (by CPCTC),

must be a right angle(similar arguments can be given for the remaining angles of parallelogram MPON). Therefore parallelogram MPON is a square.

RETURN