91Ó°ÊÓ

State and prove the converse of the Pythagorean Theorem analytically.

Prove analytically that the lines joining the midpoints of the adiacent sides of any quadrilateral form a parallelogram.

Prove, in the framework of coordinate geometry, that the sum of the squares of the distances from any point in the plane to two opposite vertices of any rectangle is equal to the sum of the squares of its distances from the other two vertices.