Hierarchy of Quadrilaterals
- Alec Arnone
Quadrilaterals: Trapezoid, Parallelogram, Kite, Rectangle, Rhombus & Square
Below are 6 different quadrilaterals: Trapezoid, Parallelogram, Kite, Rectangle, Rhombus & Square. Observe the properties of the sides, angles (opposing angles, congruent, supplementary, complimentary, total), diagonals (perpendicular, bisect, congruent) and the properties of the symmetry (line and point).
Trapezoid (BLUE), Parallelogram (GREEN), Rhombus (RED), Kite (PURPLE), Rectangle (PINK), Square (YELLOW)
After observing the different quadrilaterals it is time to do some further investigating in order to create a tree or web diagram that accurately illustrates the hierarchy of these quadrilaterals. We need to determine which shapes can be considered other shapes and which ones are in a category of their own. We know one thing, they are all quadrilaterals so (hint, hint) quadrilateral goes at the top of our tree. Here are some things to pay attention to: 1. The properties of the sides: a. Grab a corner and drag the shape around. How do the sides change, are they congruent? Are they parallel? Do the sides stay proportionate to one another when you change the size of the shape? 2. The properties of the angles: a. How do the angles change when you move the shapes around? How are the opposite angles similar or different? Are they consecutive or supplementary? Is there a right angle? If so, how many? Can you make a right angle by moving the shape around or change an existing right angle to a different angle? Can you change an angle to make it obtuse or acute or vice versa? 3. The Properties of the Diagonals: a. Are the diagonals perpendicular (create a 90 degree angle)? Are the diagonals bisected by the other or not (cut the shape in half)? Are they congruent or not? 4. The Properties of Symmetry (Line and Point): a. If you were to fold the shape in half from any point does it fold perfectly in half? If you were to rotate the shape at which degrees does it return to its normal position (90, 180, 270, 360)? 5. EXTRA HELP: a. Move the shapes on top of each other. Do the shapes line up? Do any of the sides line up? Are the angles similar? Can you manipulate a shape to fit inside another shape? b. HINT: The Kite is picky for a reason, it is very unique. 6. BONUS POINTS a. What minimal definitions can you come up with for the shapes? These definitions must be unique to the point where it could only describe one shape. Manipulate the shapes to try and disprove your definitions so you know they are true.
5.G.B.4: Classify two-dimensional figures in a hierarchy based on properties.