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Home > GC > Chapter 8 > Lesson 8.1.1 > Problem 8-11


Decide if the following statements are true or false. If a statement is false, provide a diagram of a counterexample.  

Consider the definitions of the polygons, not just the typical examples.
If necessary, review definitions in the glossary.

  1. All squares are rectangles.

    True, a rectangle is a quadrilateral with four right angles and a square is a quadrilateral with four right angles and four congruent sides.

  2. All quadrilaterals are parallelograms.

    False, quadrilaterals can exist without parallel sides, like a kite or a trapezoid.
    Remember a parallelogram has 2 sets of parallel sides.

  3. All rhombi are parallelograms.

  4. All squares are rhombi.

  5. The diagonals of a parallelogram bisect the angles.