Open Middle: Building Special Quadrilaterals

Tim Brzezinski, Jul 1, 2020

Here, a collection of Open Middle themed problems where students build special quadrilaterals in the coordinate plane so vertices have no repeated coordinates. Students also use GeoGebra tools to justify and then explain why the special quadrilaterals they construct are correct.

Table of Contents

  1. Special Parallelograms
    1. Open Middle: Building Parallelograms
    2. Open Middle: Building Rectangles
    3. Open Middle: Building Rhombuses
    4. Open Middle: Building Squares
  2. Other Quadrilaterals
    1. Open Middle: Building Trapezoids
    2. Open Middle: Building Isosceles Trapezoids
    3. Open Middle: Building Kites

1.

Special Parallelograms

  • 1. Open Middle: Building Parallelograms
  • 2. Open Middle: Building Rectangles
  • 3. Open Middle: Building Rhombuses
  • 4. Open Middle: Building Squares

1.1.

Open Middle: Building Parallelograms

YOUR TASK:
Move points A, B, C, and/or D to create a parallelogram below. Be sure NO COORDINATE REPEATS!
In the app above, use any one (or more) GeoGebra tools to clearly show how you know the quadrilateral you just formed is a parallelogram. Below, explain how what you did above illustrates how your quadrilateral is a parallelogram.
Move points A, B, C, and/or D to create a different parallelogram from the one you created above. Be sure NO COORDINATE REPEATS!
In the app above, use any one (or more) GeoGebra tools to clearly show how you know the quadrilateral you just formed is a parallelogram. Below, explain how what you did above illustrates how your quadrilateral is a parallelogram.
– Tim Brzezinski

1.2.

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1.3.

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1.4.

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2.

Other Quadrilaterals

  • 1. Open Middle: Building Trapezoids
  • 2. Open Middle: Building Isosceles Trapezoids
  • 3. Open Middle: Building Kites

2.1.

Open Middle: Building Trapezoids

Here is a quadrilateral that is said to be a trapezoid. (Be sure to drag A, B, C, D around).
Without Googling, complete the following sentence definition: [br][br]A [b]trapezoid[/b] is a quadrilateral with ...
YOUR TASK:
The quadrilateral below has 4 vertices. [br]Each vertex has 2 coordinates ([i]x[/i], [i]y[/i]). [br][br][b]Your task:[/b] Construct a quadrilateral in the app below so that [br][list][*]Coordinates take on integer values 0 - 9 [/*][*]There are [i]no repeated coordinates[/i] [/*][*]The quadrilateral formed is a [i][b]trapezoid [/b][/i][/*][/list][br][b]Note: [/b]Repeated coordinates, if any, are displayed to the right.
Create a trapezoid below. Be sure the vertices have no repeated coordinates!
Use any GeoGebra tool(s) in the app above to clearly show how you know the quadrilateral you just formed is a trapezoid. Be sure to fully explain your reasoning!
Create another trapezoid different from the one you created above. Be sure the vertices have no repeated coordinates!
Use any GeoGebra tool(s) in the app above to clearly show how you know the quadrilateral you just formed is a trapezoid. Be sure to fully explain your reasoning!
– Tim Brzezinski

2.2.

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2.3.

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