ABCD is a rectangle .Prove that ABCD is a square.

Definition: A rectangle is a quadrilateral with all four angles right angles.

From this definition you can prove that the opposite sides are parallel and of the same lengths. A rectangle can be tall and thin, short and fat or all the sides can have the same length.

Definition: A square is a quadrilateral with all four angles right angles and all four sides of the same length.

So a square is a special kind of rectangle, it is one where all the sides have the same length. Thus every square is a rectangle because it is a quadrilateral with all four angles right angles. However not every rectangle is a square, to be a square its sides must have the same length.