MUST BE / COULD BE

Here are some more challenges from Mr. Quincey. For each description of a quadrilateral below, say what special type the quadrilateral must be and/or what special type the quadrilateral could be. Look out: Some descriptions may have no “must be”s, and some descriptions may have many “could be”s!  

1. “My quadrilateral has a pair of equal sides and a pair of parallel sides.”

   Hint (a):

   How many sides does this shape have? Which shapes have these same characteristics?

2. “The diagonals of my quadrilateral bisect each other.”

   Hint (b):

   What shapes have these characteristics?

   Answer (b):

   Must be: parallelogram because all parallelograms have bisecting diagonals.
   Could be: rhombus, rectangle, and square, because they have bisecting diagonals, but other properties are necessary to be these shapes.