Hello everyone,

I am having trouble writing down the exact proofs of these two questions:

1. The four bisections of a parallelogram form a rectangle.

2. If the bisections of quadrileteral ABCD form a rectangle, ABCD is a parallelogram.

First off, here's the analysis figure:

For question 1, I have written down the following:

AB // DC => Angle BAC + Angle ADC = 180^{o}. α + δ = 90^{o}. => Angle ASD = 90^{o}

The same can now be done with Angle CQB. However, Angles R and P are not in triangles, so I'm stuck there.

For question 2, I obviously give the reverse proof, starting from Angle ASD being 90^{o}and then reading backwards from question 1, but I have the same problem with angles P and R as I had with question 1.

If anyone could help me with this, thanks a lot!