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