Quadrilaterals

Tim Brzezinski, Judi Nagel, Nov 2, 2017

Properties of Special Quadrilaterals

Table of Contents

  1. Scaffolded Discovery Templates
    1. Parallelograms (I)
    2. Parallelogram Template (Scaffolded Discovery)
    3. Quadrilateral With Opposite Angles Congruent
    4. Parallelogram Diagonals
    5. Rectangle Action!
    6. Rectangle Diagonals
    7. Rectangle Template (Scaffolded Investigation)
    8. Rhombus Action!
    9. Rhombus Diagonals
    10. Rhombus Template (Scaffolded Discovery)
    11. Square Action!
    12. Trapezoid Median (Midsegment) Action!
    13. Trapezoid Median: 2 Discoveries
    14. Isosceles Trapezoid Action!
    15. Isosceles Trapezoid Template (Scaffolded Discovery)
    16. Isosceles Trapezoid Diagonals
    17. Isosceles Trapezoid Midpoints
  2. Quadrilaterals: Angles
    1. Quadrilateral Angle Theorems
    2. Exterior Angles of a Quadrilateral
  3. Quadrilateral Theorems (Without Words)
    1. Parallelogram: Theorem 1
    2. Parallelogram: Theorem 2
    3. Parallelogram: Theorem (3)
    4. Special Quadrilateral: Theorem 1
    5. Special Quadrilateral: Theorem 2
    6. Special Quadrilateral: Theorem 3
    7. Special Quadrilateral: Theorem 4

1.

Scaffolded Discovery Templates

  • 1. Parallelograms (I)
  • 2. Parallelogram Template (Scaffolded Discovery)
  • 3. Quadrilateral With Opposite Angles Congruent
  • 4. Parallelogram Diagonals
  • 5. Rectangle Action!
  • 6. Rectangle Diagonals
  • 7. Rectangle Template (Scaffolded Investigation)
  • 8. Rhombus Action!
  • 9. Rhombus Diagonals
  • 10. Rhombus Template (Scaffolded Discovery)
  • 11. Square Action!
  • 12. Trapezoid Median (Midsegment) Action!
  • 13. Trapezoid Median: 2 Discoveries
  • 14. Isosceles Trapezoid Action!
  • 15. Isosceles Trapezoid Template (Scaffolded Discovery)
  • 16. Isosceles Trapezoid Diagonals
  • 17. Isosceles Trapezoid Midpoints

1.1.

Parallelograms (I)

[color=#000000]Please use these applets to help you complete the [/color][i][color=#0000ff]Parallelogram Investigation[/color][/i][color=#000000] questions given to you at the beginning of class. [/color]
Sides of a Parallelogram
Interior Angles of a Parallelogram
Diagonals of a Parallelogram
– Tim Brzezinski

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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1.15.

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1.16.

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1.17.

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2.

Quadrilaterals: Angles

  • 1. Quadrilateral Angle Theorems
  • 2. Exterior Angles of a Quadrilateral

2.1.

Quadrilateral Angle Theorems

Interact with the app below for a few minutes.  [br]Then, answer the questions that follow.  [br][br]Be sure to change the locations of this quadrilateral's vertices each time [i]before[/i] you drag the slider!
Into how many non-overlapping triangles were we able to split this quadrilateral?
What is the sum of the measures of the interior angles of [i]each triangle[/i]?
Use your responses from the two questions above to [b]determine the sum of the measures of the interior angles of this quadrilateral. [/b]
What is the [b]sum of the measures of the exterior angles[/b] of this quadrilateral?
– Tim Brzezinski

2.2.

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3.

Quadrilateral Theorems (Without Words)

  • 1. Parallelogram: Theorem 1
  • 2. Parallelogram: Theorem 2
  • 3. Parallelogram: Theorem (3)
  • 4. Special Quadrilateral: Theorem 1
  • 5. Special Quadrilateral: Theorem 2
  • 6. Special Quadrilateral: Theorem 3
  • 7. Special Quadrilateral: Theorem 4

3.1.

Parallelogram: Theorem 1

Interact with the applet below for a few minutes. [br]Then, answer the questions that follow. [br][br]Feel free to move the BIG WHITE POINTS anywhere you'd like! [br][color=#ff00ff]You can also adjust the size of the pink angle by using the slider. [/color]
1.
What special type of quadrilateral was formed in the first half of your sliding-the-slider? How do you know this?
2.
What else can you conclude about this special type of quadrilateral? Be specific!
3.
Write a 2-column, paragraph, or coordinate geometry proof of what you've informally observed here. (Hint: If you choose a 2-column or paragraph proof, this proof will involve a pair of congruent triangles!)
Quick Demo: 0:00 sec to 0:33 sec (BGM: Andy Hunter)
– Tim Brzezinski

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3.3.

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3.5.

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3.6.

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3.7.

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Information