Quadrilateral Graphic Organizers
What statements can we make based on the diagram to
the left?
Examples:
o All parallelograms are quadrilaterals
o All rhombuses squares and rectangles are
parallelograms
o Some parallelograms are rhombuses, squares and
rectangles
o All squares are rhombuses and rectangles
o Some rhombuses are squares
o Some rectangles are squares
Parallelogram family tree
Each shape can be thought of as an “ancestor” of all of the
shapes below. This organizer shows that rectangles and
rhombuses are always parallelograms and that the square is
always both a rectangle and a rhombus.
Like a family tree, it does not work backwards, for instance, you
cannot say that a parallelogram is always a rhombus or a
rectangle is always a square. If you go backwards you have to
use “sometimes” instead of “always.”
Trapezoid
Properties of Quadrilaterals
Parallelogram- A parallelogram is any quadrilateral (4-sided figure) with parallel and
congruent opposite sides. Rectangles, rhombuses and squares are the 3 types of special
parallelograms.
1. Defining characteristic 1: Opposite sides are parallel
2. Defining characteristic 2: Opposite sides are congruent
3. Diagonals bisect each other
4. Opposite angles are congruent
5. Consecutive angles are supplementary
Special Parallelograms: All of the figures below are also parallelograms. Note: all of the
properties of parallelograms apply to each of the special parallelograms below.
1. Rectangle 1. Defining characteristic: 4 right angles
2. Diagonals are congruent
2. Rhombus 1. Defining characteristic: all sides are congruent
2. Diagonals bisect angles
3. Diagonals are perpendicular
3. Square 1. Defining characteristic 1: 4 right angles
2. Defining characteristic 2: All sides congruent
3. Diagonals are congruent
4. Diagonals bisect angles
5. Diagonals are perpendicular