2. given a circle and a rectangle, what must be true about the rectangle for it to be possible to inscribe a congruent copy of it in the circle?

  The diagonal of the rectangle must be equal to the diameter of the circle.

Step-by-step explanation:

The point where the diagonals of a rectangle cross will be the center of a circumscribing circle. Obviously, the vertices of the rectangle lie on the circle, so either diagonal will be a diameter of the circle.

In order for it to be possible to inscribe a rectangle in a circle, its diagonal measure must match the diameter of the circle.

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this