Quadrilaterals

Tim Brzezinski, Sep 17, 2015

Properties of Special Quadrilaterals

Table of Contents

  1. Blank Templates
    1. Parallelogram Template
    2. Rhombus Template with Investigation Questions
    3. Rectangle Template with Investigation Questions
    4. Square Template with Investigation Questions
    5. Isosceles Trapezoid Template
    6. Kite Template with Investigation Questions
    7. Trapezoids: Median Investiagtion
  2. Scaffolded Discovery Templates
    1. Parallelograms (I)
    2. Parallelogram Template (Scaffolded Discovery)
    3. Parallelogram Construction Template & Discovery Lab
    4. What Kind of Quadrilateral is This? (Part 1)
    5. What Kind of Quadrilateral is This? (Part 2)
    6. What Kind of Quadrilateral is This? (Part 3)
    7. What Kind of Quadrilateral is This? (Part 4)
    8. Quadrilateral With Opposite Angles Congruent
    9. Parallelogram Diagonals
    10. What Kind of Quad?
    11. Quadrilateral Investigation (I)
    12. Rectangle Action!
    13. Rectangle Diagonals
    14. Rectangle Template (Scaffolded Investigation)
    15. Rhombus Action!
    16. Rhombus Diagonals
    17. Rhombus Template (Scaffolded Discovery)
    18. Square Action!
    19. Trapezoid Median (Midsegment) Action!
    20. Trapezoid Median: 2 Discoveries
    21. Isosceles Trapezoid Action!
    22. Isosceles Trapezoid Template (Scaffolded Discovery)
    23. Kite Action!
    24. Kite Template: Scaffolded Investigation
    25. Isosceles Trapezoid Diagonals
    26. Isosceles Trapezoid Midpoints
    27. Quad Midpoints Action!
    28. Quadrilateral Creation Templates
    29. Quadrilateral Creations from 2 Isosceles Triangles
  3. Quadrilaterals: Angles
    1. Quadrilateral Angle Theorems
    2. Exterior Angles of a Quadrilateral
  4. 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
    8. Obvious Trapezoid Theorem?

1.

Blank Templates

  • 1. Parallelogram Template
  • 2. Rhombus Template with Investigation Questions
  • 3. Rectangle Template with Investigation Questions
  • 4. Square Template with Investigation Questions
  • 5. Isosceles Trapezoid Template
  • 6. Kite Template with Investigation Questions
  • 7. Trapezoids: Median Investiagtion

1.1.

Parallelogram Template

Parallelogram Lab
Use GeoGebra to complete the following investigation. [b]BE SURE to move the vertices and sides of this parallelogram around after completing each step in order to help you make more informed conjectures[/b]: [br][br]1) Measure and display the lengths of all 4 sides. What, if anything, do you notice? Describe in detail. [br]2) Construct the midpoint of segment AC (even though you haven’t constructed segment AC yet.) Label this point “E”. [br]3) Construct segments with lengths AE, BE, CE, & DE. Then measure and display their lengths. What do you notice? Describe in detail. [br]4) Measure & display the measures of the following angles: Angle BAE, EAD, ADE, EDC, DCE, ECB, CBE, EBA. What do you notice? Describe in detail. [br]5) Measure display just one of the four angles you see with vertex E. [br]6) Construct polygon (triangle) ABC. Then reflect this polygon about diagonal AC.[br]7) Use GeoGebra to “UNDO” step (6) and step (5). Now construct polygon (triangle) DBA. Then reflect this polygon about diagonal DB. [br][br]Questions to answer/consider: [br][br]1) Are opposite sides of a parallelogram congruent? [br]2) Are opposite angles (ENTIRE ANGLES—like angle DAB & angle DCB) of a parallelogram congruent?[br]3) Do the diagonals of a parallelogram bisect EACH OTHER?[br]4) Does a diagonal of an parallelogram bisect a pair of opposite angles? If so, how many diagonals do this? [br]5) Are the diagonals of a parallelogram perpendicular? [br]6) Are the diagonals of a parallelogram congruent?[br]7) Does either diagonal of a parallelogram serve as a line of symmetry? If so, how many?
– Tim Brzezinski

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1.6.

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1.7.

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2.

Scaffolded Discovery Templates

  • 1. Parallelograms (I)
  • 2. Parallelogram Template (Scaffolded Discovery)
  • 3. Parallelogram Construction Template & Discovery Lab
  • 4. What Kind of Quadrilateral is This? (Part 1)
  • 5. What Kind of Quadrilateral is This? (Part 2)
  • 6. What Kind of Quadrilateral is This? (Part 3)
  • 7. What Kind of Quadrilateral is This? (Part 4)
  • 8. Quadrilateral With Opposite Angles Congruent
  • 9. Parallelogram Diagonals
  • 10. What Kind of Quad?
  • 11. Quadrilateral Investigation (I)
  • 12. Rectangle Action!
  • 13. Rectangle Diagonals
  • 14. Rectangle Template (Scaffolded Investigation)
  • 15. Rhombus Action!
  • 16. Rhombus Diagonals
  • 17. Rhombus Template (Scaffolded Discovery)
  • 18. Square Action!
  • 19. Trapezoid Median (Midsegment) Action!
  • 20. Trapezoid Median: 2 Discoveries
  • 21. Isosceles Trapezoid Action!
  • 22. Isosceles Trapezoid Template (Scaffolded Discovery)
  • 23. Kite Action!
  • 24. Kite Template: Scaffolded Investigation
  • 25. Isosceles Trapezoid Diagonals
  • 26. Isosceles Trapezoid Midpoints
  • 27. Quad Midpoints Action!
  • 28. Quadrilateral Creation Templates
  • 29. Quadrilateral Creations from 2 Isosceles Triangles

2.1.

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

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2.7.

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2.10.

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2.11.

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2.12.

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2.13.

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2.14.

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2.15.

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2.16.

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2.17.

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2.18.

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2.19.

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2.20.

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2.21.

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2.22.

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2.23.

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2.24.

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2.25.

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2.26.

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2.27.

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2.28.

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2.29.

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3.

Quadrilaterals: Angles

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

3.1.

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

3.2.

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4.

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
  • 8. Obvious Trapezoid Theorem?

4.1.

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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4.8.

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Information