Quadrilateral Family
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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.

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.]

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

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

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

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

A rhombus is a slanted square.  It has all of the properties of a parallelogram plus three additional properties.

 

*Square
Hey, look at me!
I have all of the properties of the parallelogram AND the rectangle AND the rhombus.
I have it all!

The square is the most specific member of the quadrilateral family.  It has the largest number of properties.