Decide if the following statements are true or false. If a statement is true, explain how you know it is always true. If a statement is false, provide a diagram or a description of a counterexample.

1. If the diagonals of a quadrilateral are congruent, then it is a rectangle.

   Hint (a):

   Can you draw a quadrilateral with congruent diagonals that is not a rectangle?

2. If a quadrilateral has four congruent angles, then it is a rectangle.

   Hint (b):

   What kinds of quadrilaterals have four congruent angles?

3. All rhombi are parallelograms.

4. The diagonals of a parallelogram bisect the angles.