Quadrilaterals and Polygons: Squares, Rectangles and Rhombi

Similarities Between Properties of Squares, Rectangles and Rhombi

You may have noticed that many of the properties of these three parallelograms are the same.  Let’s look at these similarities.

 

A square is a rhombus, because a square must have the three properties that a rhombus has:

• All four sides are congruent

• Diagonals are perpendicular

• Diagonals bisect each angle


 


A rhombus, however, may  NOT be a square, because a rhombus may not have two of the properties a square has:

    • All four angles do not have to be congruent in a rhombus
    • Diagonals do not have to be congruent in a rhombus

 

When a parallelogram has all five properties, it can be called a square, and it can also be called a rhombus. 

A square is a rectangle, because a square must have the two properties that a rectangles has:

  • All four angles are congruent (90°)
  • Diagonals are congruent


 

A rectangle, however, may NOT be a square, because a rectangle may not have three of the properties a square has:

    • All four sides may not be congruent
    • Diagonals may not be perpendicular
    • Diagonals may not bisect each angle

 

When a parallelogram has all five properties, it can be called a square, and it can also be called a rectangle.