Quadrilateral Family

Quadrilateral Family

Each member of the quadrilateral family will describe its specific properties.

Quadrilateral

  • I have exactly four sides.
  • The sum of the interior angles of all quadrilaterals is 360º.
    Quadrilateral Family 1
  • A quadrilateral is any four sided figure. Do not assume any additional properties for a quadrilateral unless you are given additional information.

Trapezoid

  • I have only one set of parallel sides.
    [The median of a trapezoid is parallel to the bases and equal to one-half the sum of the bases.]
    Quadrilateral Family 2
  • A trapezoid has ONLY ONE set of parallel sides. When proving a figure is a trapezoid, it is necessary to prove that two sides are parallel and two sides are not parallel.

Isosceles Trapezoid

  • I have: only one set of parallel sides
  • base angles congruent
  • legs congruent
  • diagonals congruent
  • opposite angles supplementary
    Quadrilateral Family 3
  • Never assume that a trapezoid is isosceles unless you are given (or can prove) that information.

Parallelogram

  • I have: 2 sets of parallel sides
  • 2 sets of congruent sides
  • opposite angles congruent
  • consecutive angles supplementary
  • diagonals bisect each other
  • diagonals form 2 congruent triangles
    Quadrilateral Family 4
  • Notice how the properties of a parallelogram come in sets of twos: two properties about the sides; two properties about the angles; two properties about the diagonals. Use this fact to help you remember the properties.

Rectangle

  • I have all of the properties of the parallelogram PLUS
  • 4 right angles
  • diagonals congruent
    Quadrilateral Family 5
  • If you know the properties of a parallelogram, you only need to add 2 additional properties to describe a rectangle.

Rhombus

  • I have all of the properties of the parallelogram PLUS
  • 4 congruent sides
  • diagonals bisect angles
  • diagonals perpendicular
    Quadrilateral Family 6
  • A rhombus is a slanted square. It has all of the properties of a parallelogram plus three additional properties.

Square

  • I have all of the properties of the parallelogram AND the rectangle AND the rhombus.
    Quadrilateral Family 7
  • The square is the most specific member of the quadrilateral family. It has the largest number of properties.