Quadrilateral Family Topic Index | Geometry Index | Regents Exam Prep Center

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.

 *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.

 Topic Index | Geometry Index | Regents Exam Prep Center Created by Donna Roberts