Congruence (Vol 2)

Tim Brzezinski, Sep 30, 2016

Table of Contents

  1. Lines and Angles
    1. Exploring Points, Lines, and Planes (V1)
    2. Exploring Points, Lines, and Planes (V2)
    3. Where Did the Plane Go?
    4. Measuring Length with a Centimeter Ruler
    5. Segment Addition Postulate: Formative Assessment
    6. Midpoint Theorem: Formative Assessment
    7. Measuring Angles with a Protractor
    8. Angle Sketching by Estimation
    9. Angle Addition Postulate: Formative Assessment
    10. Angle Bisector Theorem: Formative Assessment
    11. Open Middle Problem: Complementary and Supplementary Angles
    12. Open Middle: Supplementary Angles
    13. Vertical Angles: Quick Exploration
    14. Vertical Angles Exploration (1)
    15. Vertical Angles Exploration (2)
    16. Vertical Angles: Quick Discovery
    17. Vertical Angles Theorem
    18. Animation 1
    19. Transversal Intersects Parallel Lines
    20. Transversals, Parallel Lines, Angles: Protractor Version
    21. Corresponding Angles: Quick Investigation
    22. Congruent Corresponding Angles to Start? (Quick Investigation)
    23. Exploring Corresponding Angles (V2)
    24. Alternate Interior Angles: Quick Investigation
    25. Alternate Interior Angles Theorem (V1)
    26. Exploring Alternate Interior Angles (V2)
    27. Alternate Interior Angles Theorem (V3)
    28. Animation 16
    29. Alternate Exterior Angles: Quick Investigation
    30. Alternate Exterior Angles Theorem (V1)
    31. Exploring Alternate Exterior Angles (V2)
    32. Animation 39
    33. Animation 60
    34. Same-Side-Interior Angles: Quick Investigation
    35. Same Side Interior Angles Theorem
    36. Animation 29
    37. Same-Side-Exterior Angles: Quick Investigation
    38. Exploring Same Side Exterior Angles
    39. Animation 73
    40. Parallel Lines and Angle Measures (1)
    41. Parallel Lines and Angle Measures (2)
    42. Open Middle: Same-Side Interior or Exterior Angles
    43. Open Middle Challenge: Parallel Lines and Related Angles
    44. Solution to Parallel Lines & Angles Problem
    45. Interesting Coplanar Locations (1)
    46. A Special Theorem: Part 1 (V1)
    47. A Special Theorem: Part 2 (V1)
    48. A Special Theorem: Part 2 (V2)
    49. A Special Theorem: Part 2 (V3)
    50. Animation 57
    51. Perpendicular Bisector: Quick Recap
    52. A Special Theorem: Part 2 (V4)
    53. PBT (Part 1) - Quick
    54. PBT (Part 2) - Quick
    55. Plane Bisector: Quick Illustrator
    56. Where in This City? (1)
    57. CT Home Depots
    58. Where in NYC? (VA)
    59. Where in NYC? (VB)
    60. Where in NYC? (VC)
    61. Angle Bisector Theorem (Part 1)
    62. Another Special Theorem: Part 1 (V1)
    63. Another Special Theorem: Part 2 (V1)
    64. Another Special Theorem: Part 1 (V2)
    65. Animation 58
    66. Another Special Theorem: Part 1 (V3)
    67. Effortless Trisections
    68. Animation 134
    69. Parallel Lines Congruent Segments Theorem
    70. Parallel Lines Proportionality Theorem
    71. Animation 135
    72. Proof Prompt (A)
    73. Animation 128
    74. Proof Prompt (B)
    75. Animation 127
    76. Proof Prompt (C)
    77. Animation 131
    78. Proof Prompt (D)
    79. Animation 130
  2. Triangles & Polygons
    1. Triangle Area Action! (V1)
    2. Triangle Area Action!!! (V2)
    3. Open Middle: Triangle Area Problem
    4. Animation 175
    5. Area of a Triangle (Discovery)
    6. 4 Triangles Action!!!
    7. Animation 179
    8. Triangle Angle Theorems
    9. Animation 171
    10. Animation 2
    11. Triangle Angle Theorems (V3)
    12. Triangle Angle Sum Theorem (V4)
    13. Open Middle: Triangle Angles
    14. Open Middle Triangle Angles Problem
    15. Open Middle Triangle Angle Sum Problem
    16. Open Middle Triangle Angle Sum Problem (V2)
    17. Triangle Angle Sum Theorem
    18. Obvious Corollary
    19. Animation 140
    20. Triangle Exterior Angle
    21. Animation 102
    22. Triangle: Exterior Angles
    23. Open Middle: Interior and Exterior Angles of Triangles
    24. Quadrilateral: Exterior Angles
    25. Pentagon: Exterior Angles
    26. Polygons: Exterior Angles
    27. Polygons: Exterior Angles - REVAMPED
    28. Exterior Angles (Revisited)
    29. Exterior Angles (Revisited) V2
    30. Lambourghini Turning Angles
    31. Exploring Polygon Angles: Triangle through Octagon
    32. Angles of a Right Triangle
    33. Animation 104
    34. Acute Angles of a Right Triangle
    35. Animation 129
    36. Animation 22
    37. Isosceles Triangle: Quick Discovery
    38. IST: Quick Discovery (Revamped)
    39. A Special Triangle & Its Properties (I)
    40. Isosceles Triangle Investigation
    41. Isosceles Triangle Theorem: Discovery Lab
    42. Animation 8
    43. Exploring Isosceles Triangles (Version A)
    44. Exploring Isosceles Triangles (VB)
    45. Converse of IST: Template
    46. Converse of IST (V1)
    47. One Special Triangle: Quick Investigation
    48. Animation 82
    49. Controlling Angles with Sliders: Ex. 14
    50. Animation 23
    51. Another Special Triangle and its Properties (II)
    52. Animation 27
    53. Converse of IST (II)
    54. Animation 84
    55. Isosceles Right Triangle: Quick Investigation
    56. Special Right Triangle (I)
    57. Animation 59
    58. Special Right Triangle (II)
    59. Another Special Right Triangle (Guided Discovery)
    60. Animation 42
    61. Special Line through Triangle V1 (Theorem Discovery)
    62. Special Line through Triangle V2 (Theorem Discovery)
    63. Triangle Midsegment Action!
    64. Animation 141
    65. Working With Midpoints: Ex. 8
    66. Midsegment of a Triangle
    67. Triangle Inequality: Open Middle Problem (V1)
    68. Triangle Inequality: Open Middle Problem (V2)
    69. Triangle Inequality: Discovery Lesson
    70. Triangle Side Possibilities? (V2)
    71. Triangle Inequality
    72. Triangle Inequality (II)
    73. Sliders & Circles Discovery: Ex. 13
    74. Inequalities in 1 Triangle
    75. Points of Concurrency: Investigation
    76. Lines Containing Altitudes of a Triangle (V1)
    77. Orthocenter Exploration
    78. Guess the Orthocenter!
    79. Circumcenter (& Questions)
    80. Circumcenter & Circumcircle Action!
    81. Making Perpendicular Bisectors: Ex. 9
    82. Guess the Circumcenter!
    83. Animation 28
    84. Midpoint of HYP
    85. Animation 46
    86. Incenter Exploration (A)
    87. Incenter Exploration (B)
    88. Incenter + Incircle Action (V2)!
    89. Incenter & Incircle Action!
    90. Constructing Angle Bisectors: Ex. 11
    91. Guess the Incenter!
    92. Animation 17
    93. Triangle: 3 Medians Investigation
    94. Triangle Medians: Quick Investigation
    95. Medians Centroid Theorem (Proof without Words)
    96. Medians and Centroid Dance
    97. Guess the Centroid!
    98. Animation 25
    99. Right Triangle Investigation
  3. Parallelograms
    1. Parallelogram: Area
    2. Animation 202
    3. Parallelogram Construction Template & Discovery Lab
    4. Parallelogram Template (Scaffolded Discovery)
    5. Parallelogram: Theorem 1
    6. Animation 123
    7. Parallelogram: Theorem 2
    8. Animation 124
    9. Parallelogram: Theorem (3)
    10. Animation 125
    11. Parallelograms (I)
    12. Animation 75
    13. Animation 80
    14. Animation 6
    15. What Kind of Quadrilateral is This? (Part 1)
    16. What Kind of Quadrilateral is This? (Part 2)
    17. What Kind of Quadrilateral is This? (Part 3)
    18. What Kind of Quadrilateral is This? (Part 4)
    19. Special Quadrilateral: Theorem 1
    20. Animation 184
    21. Special Quadrilateral: Theorem 2
    22. Animation 185
    23. Special Quadrilateral: Theorem 3
    24. Animation 186
    25. Special Quadrilateral: Theorem 4
    26. Animation 187
    27. Congruent Opposite Sides of a Quadrilateral
    28. Quadrilateral With Opposite Angles Congruent
    29. What Kind of Quad?
    30. Quadrilateral Investigation (I)
    31. Rhombus Action!
    32. Animation 11
    33. Rhombus Construction Template
    34. Rhombus Template with Investigation Questions
    35. Rhombus Template (Scaffolded Discovery)
    36. Area of a Rhombus
    37. Rectangle Action!
    38. Animation 31
    39. Rectangle Construction Template
    40. Rectangle Template (Scaffolded Investigation)
    41. Rectangle Template with Investigation Questions
    42. Square Construction Template (1)
    43. Square Construction Template (2)
    44. Square Template (Scaffolded Investigation)
    45. Square Template with Investigation Questions
    46. Square Action!
    47. Animation 41
    48. Trapezoid Construction Template
    49. Trapezoids: Median Investiagtion
    50. Trapezoid Median (Midsegment) Action!
    51. Animation 67
    52. Trapezoid Median: 2 Discoveries
    53. Isosceles Trapezoid Action!
    54. Animation 64
    55. Animation 35
    56. Isosceles Trapezoid Construction Template
    57. Isosceles Trapezoid Template (Scaffolded Discovery)
    58. Isosceles Trapezoid Template
    59. Animation 49
    60. Obvious Trapezoid Theorem?
    61. Kite Action!
    62. Animation 26
    63. Kite Construction Template (2)
    64. Kite Template: Scaffolded Investigation
    65. Kite Template with Investigation Questions
    66. Quad Midpoints Action!
    67. Animation 52
    68. Quadrilateral Creation Templates
    69. Quadrilateral Creations from 2 Isosceles Triangles
  4. Geometric constructions
    1. Congruent Segments Construction (I)
    2. Isosceles Triangle (Quick Construction Technique) V1
    3. Animation 199
    4. Equilateral Triangle Construction (Dynamic Illustration)
    5. Animation 201
    6. Congruent Angle: Construction
    7. Congruent Angle Construction Action!
    8. Animation 196
    9. Angle Bisector Construction Action!
    10. Animation 197
    11. Alternate Angle Bisector Construction
    12. Animation 117
    13. Angle Bisector: Construction
    14. Angle Bisector (Basic Exercise)
    15. Perpendicular Line: Construction 1
    16. Perpendicular Line: Construction 2
    17. Perpendicular Bisector: Construction
    18. Parallel Line: Constructions
    19. Congruent Triangle: Construction
    20. Rectangle Construction Exercise
    21. Rectangle Construction Exercise: Revamped (V1)
    22. Rectangle Construction Exercise: Revamped (V2)
    23. Rhombus Construction Exercise: V1
    24. Rhombus Construction Exercise: V2
    25. Other Constructions: 1
    26. Other Constructions: 2
    27. Centroid Construction Challenge #1
    28. Possible Solution for Centroid Challenge #1
    29. Centroid Construction Challenge #2
    30. Possible Solution for Centroid Construction Challenge #2
    31. Centroid Construction Challenge #3
    32. Possible solution to Centroid Construction Challenge #3
    33. Triangle Construction Challenge #1
    34. Possible solution to Triangle Construction Challenge #1
    35. Triangle Consruction Challenge #2
    36. Possible solution to Triangle Construction Challenge #2
    37. Triangle Construction Challenge #3
    38. Potential solution for Triangle Construction Challenge #3
    39. Geometric Mean Illustration
    40. Animation 211
    41. Geometric Mean: Construction (VA)
    42. Geometric Mean: Construction (VB)
  5. Constructing Regular Polygons Inscribed in Circles
    1. Equilateral Triangle Construction Template
    2. Creating Regular Polygons: Ex. 1
    3. Using Circle and Intersect Tools: Ex. 2
    4. Using the Compass Tool: Ex. 3
    5. Square Construction Template
    6. Regular Hexagon Construction Template
  6. Other Geometry Resources
    1. Geometry Resources

1.

Lines and Angles

  • 1. Exploring Points, Lines, and Planes (V1)
  • 2. Exploring Points, Lines, and Planes (V2)
  • 3. Where Did the Plane Go?
  • 4. Measuring Length with a Centimeter Ruler
  • 5. Segment Addition Postulate: Formative Assessment
  • 6. Midpoint Theorem: Formative Assessment
  • 7. Measuring Angles with a Protractor
  • 8. Angle Sketching by Estimation
  • 9. Angle Addition Postulate: Formative Assessment
  • 10. Angle Bisector Theorem: Formative Assessment
  • 11. Open Middle Problem: Complementary and Supplementary Angles
  • 12. Open Middle: Supplementary Angles
  • 13. Vertical Angles: Quick Exploration
  • 14. Vertical Angles Exploration (1)
  • 15. Vertical Angles Exploration (2)
  • 16. Vertical Angles: Quick Discovery
  • 17. Vertical Angles Theorem
  • 18. Animation 1
  • 19. Transversal Intersects Parallel Lines
  • 20. Transversals, Parallel Lines, Angles: Protractor Version
  • 21. Corresponding Angles: Quick Investigation
  • 22. Congruent Corresponding Angles to Start? (Quick Investigation)
  • 23. Exploring Corresponding Angles (V2)
  • 24. Alternate Interior Angles: Quick Investigation
  • 25. Alternate Interior Angles Theorem (V1)
  • 26. Exploring Alternate Interior Angles (V2)
  • 27. Alternate Interior Angles Theorem (V3)
  • 28. Animation 16
  • 29. Alternate Exterior Angles: Quick Investigation
  • 30. Alternate Exterior Angles Theorem (V1)
  • 31. Exploring Alternate Exterior Angles (V2)
  • 32. Animation 39
  • 33. Animation 60
  • 34. Same-Side-Interior Angles: Quick Investigation
  • 35. Same Side Interior Angles Theorem
  • 36. Animation 29
  • 37. Same-Side-Exterior Angles: Quick Investigation
  • 38. Exploring Same Side Exterior Angles
  • 39. Animation 73
  • 40. Parallel Lines and Angle Measures (1)
  • 41. Parallel Lines and Angle Measures (2)
  • 42. Open Middle: Same-Side Interior or Exterior Angles
  • 43. Open Middle Challenge: Parallel Lines and Related Angles
  • 44. Solution to Parallel Lines & Angles Problem
  • 45. Interesting Coplanar Locations (1)
  • 46. A Special Theorem: Part 1 (V1)
  • 47. A Special Theorem: Part 2 (V1)
  • 48. A Special Theorem: Part 2 (V2)
  • 49. A Special Theorem: Part 2 (V3)
  • 50. Animation 57
  • 51. Perpendicular Bisector: Quick Recap
  • 52. A Special Theorem: Part 2 (V4)
  • 53. PBT (Part 1) - Quick
  • 54. PBT (Part 2) - Quick
  • 55. Plane Bisector: Quick Illustrator
  • 56. Where in This City? (1)
  • 57. CT Home Depots
  • 58. Where in NYC? (VA)
  • 59. Where in NYC? (VB)
  • 60. Where in NYC? (VC)
  • 61. Angle Bisector Theorem (Part 1)
  • 62. Another Special Theorem: Part 1 (V1)
  • 63. Another Special Theorem: Part 2 (V1)
  • 64. Another Special Theorem: Part 1 (V2)
  • 65. Animation 58
  • 66. Another Special Theorem: Part 1 (V3)
  • 67. Effortless Trisections
  • 68. Animation 134
  • 69. Parallel Lines Congruent Segments Theorem
  • 70. Parallel Lines Proportionality Theorem
  • 71. Animation 135
  • 72. Proof Prompt (A)
  • 73. Animation 128
  • 74. Proof Prompt (B)
  • 75. Animation 127
  • 76. Proof Prompt (C)
  • 77. Animation 131
  • 78. Proof Prompt (D)
  • 79. Animation 130

1.1.

Exploring Points, Lines, and Planes (V1)

In the app below, drag the points to move the POINT, LINE, and PLANE. [br][br][i]If you click on a point before dragging it, you can change the direction to where you want to move it. [/i]
Without Googling, how would you describe the term "POINT"?
Without Googling, how would you describe the term "LINE"?
Without Googling, how would you describe the term "PLANE"?
– Tim Brzezinski

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2.

Triangles & Polygons

  • 1. Triangle Area Action! (V1)
  • 2. Triangle Area Action!!! (V2)
  • 3. Open Middle: Triangle Area Problem
  • 4. Animation 175
  • 5. Area of a Triangle (Discovery)
  • 6. 4 Triangles Action!!!
  • 7. Animation 179
  • 8. Triangle Angle Theorems
  • 9. Animation 171
  • 10. Animation 2
  • 11. Triangle Angle Theorems (V3)
  • 12. Triangle Angle Sum Theorem (V4)
  • 13. Open Middle: Triangle Angles
  • 14. Open Middle Triangle Angles Problem
  • 15. Open Middle Triangle Angle Sum Problem
  • 16. Open Middle Triangle Angle Sum Problem (V2)
  • 17. Triangle Angle Sum Theorem
  • 18. Obvious Corollary
  • 19. Animation 140
  • 20. Triangle Exterior Angle
  • 21. Animation 102
  • 22. Triangle: Exterior Angles
  • 23. Open Middle: Interior and Exterior Angles of Triangles
  • 24. Quadrilateral: Exterior Angles
  • 25. Pentagon: Exterior Angles
  • 26. Polygons: Exterior Angles
  • 27. Polygons: Exterior Angles - REVAMPED
  • 28. Exterior Angles (Revisited)
  • 29. Exterior Angles (Revisited) V2
  • 30. Lambourghini Turning Angles
  • 31. Exploring Polygon Angles: Triangle through Octagon
  • 32. Angles of a Right Triangle
  • 33. Animation 104
  • 34. Acute Angles of a Right Triangle
  • 35. Animation 129
  • 36. Animation 22
  • 37. Isosceles Triangle: Quick Discovery
  • 38. IST: Quick Discovery (Revamped)
  • 39. A Special Triangle & Its Properties (I)
  • 40. Isosceles Triangle Investigation
  • 41. Isosceles Triangle Theorem: Discovery Lab
  • 42. Animation 8
  • 43. Exploring Isosceles Triangles (Version A)
  • 44. Exploring Isosceles Triangles (VB)
  • 45. Converse of IST: Template
  • 46. Converse of IST (V1)
  • 47. One Special Triangle: Quick Investigation
  • 48. Animation 82
  • 49. Controlling Angles with Sliders: Ex. 14
  • 50. Animation 23
  • 51. Another Special Triangle and its Properties (II)
  • 52. Animation 27
  • 53. Converse of IST (II)
  • 54. Animation 84
  • 55. Isosceles Right Triangle: Quick Investigation
  • 56. Special Right Triangle (I)
  • 57. Animation 59
  • 58. Special Right Triangle (II)
  • 59. Another Special Right Triangle (Guided Discovery)
  • 60. Animation 42
  • 61. Special Line through Triangle V1 (Theorem Discovery)
  • 62. Special Line through Triangle V2 (Theorem Discovery)
  • 63. Triangle Midsegment Action!
  • 64. Animation 141
  • 65. Working With Midpoints: Ex. 8
  • 66. Midsegment of a Triangle
  • 67. Triangle Inequality: Open Middle Problem (V1)
  • 68. Triangle Inequality: Open Middle Problem (V2)
  • 69. Triangle Inequality: Discovery Lesson
  • 70. Triangle Side Possibilities? (V2)
  • 71. Triangle Inequality
  • 72. Triangle Inequality (II)
  • 73. Sliders & Circles Discovery: Ex. 13
  • 74. Inequalities in 1 Triangle
  • 75. Points of Concurrency: Investigation
  • 76. Lines Containing Altitudes of a Triangle (V1)
  • 77. Orthocenter Exploration
  • 78. Guess the Orthocenter!
  • 79. Circumcenter (& Questions)
  • 80. Circumcenter & Circumcircle Action!
  • 81. Making Perpendicular Bisectors: Ex. 9
  • 82. Guess the Circumcenter!
  • 83. Animation 28
  • 84. Midpoint of HYP
  • 85. Animation 46
  • 86. Incenter Exploration (A)
  • 87. Incenter Exploration (B)
  • 88. Incenter + Incircle Action (V2)!
  • 89. Incenter & Incircle Action!
  • 90. Constructing Angle Bisectors: Ex. 11
  • 91. Guess the Incenter!
  • 92. Animation 17
  • 93. Triangle: 3 Medians Investigation
  • 94. Triangle Medians: Quick Investigation
  • 95. Medians Centroid Theorem (Proof without Words)
  • 96. Medians and Centroid Dance
  • 97. Guess the Centroid!
  • 98. Animation 25
  • 99. Right Triangle Investigation

2.1.

Triangle Area Action! (V1)

In the applet below, [color=#38761d][b]a triangle is shown[/b][/color]. [br][br]You can change the sizes of the [b][color=#1e84cc]blue angle[/color][/b] and [color=#ff00ff][b]pink angle[/b][/color] by using the sliders in the lower-left corner. You can also move the white points anywhere you'd like at any time. [br][br]Interact with the applet below for a few minutes.[br]Then answer the questions that follow.
Area of a Triangle = ?
1.
In this applet's dynamics, the triangle was transformed into another figure. What kind of figure is it? How does the applet imply your classification is correct?
2.
How does the [b]area of the newer figure[/b] compare with the [b]area of the original triangle[/b]?
3.
How does the [b]BASE [/b]of the newer figure compare with the [b]BASE[/b] of the original triangle?
4.
How does the [color=#9900ff][b]HEIGHT[/b][/color] of the newer figure compare with the [color=#444444][b]HEIGHT[/b][/color] of the original triangle?
5.
Given your responses to (1) - (4) above, describe how you can find the area of [b][color=#38761d]ANY TRIANGLE. [/color][/b]
Quick (Silent) Demo
– Tim Brzezinski

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3.

Parallelograms

  • 1. Parallelogram: Area
  • 2. Animation 202
  • 3. Parallelogram Construction Template & Discovery Lab
  • 4. Parallelogram Template (Scaffolded Discovery)
  • 5. Parallelogram: Theorem 1
  • 6. Animation 123
  • 7. Parallelogram: Theorem 2
  • 8. Animation 124
  • 9. Parallelogram: Theorem (3)
  • 10. Animation 125
  • 11. Parallelograms (I)
  • 12. Animation 75
  • 13. Animation 80
  • 14. Animation 6
  • 15. What Kind of Quadrilateral is This? (Part 1)
  • 16. What Kind of Quadrilateral is This? (Part 2)
  • 17. What Kind of Quadrilateral is This? (Part 3)
  • 18. What Kind of Quadrilateral is This? (Part 4)
  • 19. Special Quadrilateral: Theorem 1
  • 20. Animation 184
  • 21. Special Quadrilateral: Theorem 2
  • 22. Animation 185
  • 23. Special Quadrilateral: Theorem 3
  • 24. Animation 186
  • 25. Special Quadrilateral: Theorem 4
  • 26. Animation 187
  • 27. Congruent Opposite Sides of a Quadrilateral
  • 28. Quadrilateral With Opposite Angles Congruent
  • 29. What Kind of Quad?
  • 30. Quadrilateral Investigation (I)
  • 31. Rhombus Action!
  • 32. Animation 11
  • 33. Rhombus Construction Template
  • 34. Rhombus Template with Investigation Questions
  • 35. Rhombus Template (Scaffolded Discovery)
  • 36. Area of a Rhombus
  • 37. Rectangle Action!
  • 38. Animation 31
  • 39. Rectangle Construction Template
  • 40. Rectangle Template (Scaffolded Investigation)
  • 41. Rectangle Template with Investigation Questions
  • 42. Square Construction Template (1)
  • 43. Square Construction Template (2)
  • 44. Square Template (Scaffolded Investigation)
  • 45. Square Template with Investigation Questions
  • 46. Square Action!
  • 47. Animation 41
  • 48. Trapezoid Construction Template
  • 49. Trapezoids: Median Investiagtion
  • 50. Trapezoid Median (Midsegment) Action!
  • 51. Animation 67
  • 52. Trapezoid Median: 2 Discoveries
  • 53. Isosceles Trapezoid Action!
  • 54. Animation 64
  • 55. Animation 35
  • 56. Isosceles Trapezoid Construction Template
  • 57. Isosceles Trapezoid Template (Scaffolded Discovery)
  • 58. Isosceles Trapezoid Template
  • 59. Animation 49
  • 60. Obvious Trapezoid Theorem?
  • 61. Kite Action!
  • 62. Animation 26
  • 63. Kite Construction Template (2)
  • 64. Kite Template: Scaffolded Investigation
  • 65. Kite Template with Investigation Questions
  • 66. Quad Midpoints Action!
  • 67. Animation 52
  • 68. Quadrilateral Creation Templates
  • 69. Quadrilateral Creations from 2 Isosceles Triangles

3.1.

Parallelogram: Area

Directions:
In the app below, use the [b]filling[/b] slider to make the parallelogram light enough so that you can see the white gridlines through it. [b]But don't touch anything else yet! [/b][br][br]After you set the [b]filling[/b] slider, try to count the number of squares inside this parallelogram. [br]Be sure to include partial squares! Provide a good estimate in the question box below.
Try to count the number of squares inside this parallelogram. How many squares (i.e. square units) do you estimate to be inside this parallelogram?
Slide the "[b]Slide Me" [/b]slider now. Carefully observe what happens. What shape do you see now?
How does the area of this new shape compare with the area of the original parallelogram? How do you know this?
How many squares do you now count in the newer shape that was formed? How many squares were in the original parallelogram?
Without looking it up on another tab in your browser, describe how we can find the area of ANY PARALLELOGRAM.
– Tim Brzezinski

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4.

Geometric constructions

  • 1. Congruent Segments Construction (I)
  • 2. Isosceles Triangle (Quick Construction Technique) V1
  • 3. Animation 199
  • 4. Equilateral Triangle Construction (Dynamic Illustration)
  • 5. Animation 201
  • 6. Congruent Angle: Construction
  • 7. Congruent Angle Construction Action!
  • 8. Animation 196
  • 9. Angle Bisector Construction Action!
  • 10. Animation 197
  • 11. Alternate Angle Bisector Construction
  • 12. Animation 117
  • 13. Angle Bisector: Construction
  • 14. Angle Bisector (Basic Exercise)
  • 15. Perpendicular Line: Construction 1
  • 16. Perpendicular Line: Construction 2
  • 17. Perpendicular Bisector: Construction
  • 18. Parallel Line: Constructions
  • 19. Congruent Triangle: Construction
  • 20. Rectangle Construction Exercise
  • 21. Rectangle Construction Exercise: Revamped (V1)
  • 22. Rectangle Construction Exercise: Revamped (V2)
  • 23. Rhombus Construction Exercise: V1
  • 24. Rhombus Construction Exercise: V2
  • 25. Other Constructions: 1
  • 26. Other Constructions: 2
  • 27. Centroid Construction Challenge #1
  • 28. Possible Solution for Centroid Challenge #1
  • 29. Centroid Construction Challenge #2
  • 30. Possible Solution for Centroid Construction Challenge #2
  • 31. Centroid Construction Challenge #3
  • 32. Possible solution to Centroid Construction Challenge #3
  • 33. Triangle Construction Challenge #1
  • 34. Possible solution to Triangle Construction Challenge #1
  • 35. Triangle Consruction Challenge #2
  • 36. Possible solution to Triangle Construction Challenge #2
  • 37. Triangle Construction Challenge #3
  • 38. Potential solution for Triangle Construction Challenge #3
  • 39. Geometric Mean Illustration
  • 40. Animation 211
  • 41. Geometric Mean: Construction (VA)
  • 42. Geometric Mean: Construction (VB)

4.1.

Congruent Segments Construction (I)

I[color=#000000]n the applet below, use the limited toolbar to construct segments that are congruent to the two segments displayed.[br]Use the [b]Distance[/b] tool afterwards to show that these segments are indeed congruent. [/color]
I[color=#000000]n the applet below, use the limited toolbar to construct segments that are [b]triple the length[/b] of the two segments displayed.[br]Use the [b]Distance[/b] tool afterwards to show that these segments are indeed triple the length of the original segments displayed. [/color]
– Tim Brzezinski

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5.

Constructing Regular Polygons Inscribed in Circles

  • 1. Equilateral Triangle Construction Template
  • 2. Creating Regular Polygons: Ex. 1
  • 3. Using Circle and Intersect Tools: Ex. 2
  • 4. Using the Compass Tool: Ex. 3
  • 5. Square Construction Template
  • 6. Regular Hexagon Construction Template

5.1.

Equilateral Triangle Construction Template

[color=#000000]In the applet below, use the tools of the limited toolbar to construct an [b]equilateral triangle that's inscribed in the circle shown.[/b] [br][br][i]When you're finished, show that the triangle you've constructed is indeed an equilateral triangle.[/i][/color]
– Tim Brzezinski

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6.

Other Geometry Resources

  • 1. Geometry Resources

6.1.

Geometry Resources

[list][*][b][url=https://www.geogebra.org/m/z8nvD94T]Congruence (Volume 1)[/url][/b][/*][*][b][url=https://www.geogebra.org/m/munhXmzx]Congruence (Volume 2)[/url][/b][/*][*][b][url=https://www.geogebra.org/m/dPqv8ACE]Similarity, Right Triangles, Trigonometry[/url][/b][/*][*][b][url=https://www.geogebra.org/m/C7dutQHh]Circles[/url][/b][/*][*][b][url=https://www.geogebra.org/m/K2YbdFk8]Coordinate and Analytic Geometry[/url][/b][/*][*][b][url=https://www.geogebra.org/m/xDNjSjEK]Area, Surface Area, Volume, 3D, Cross Section[/url] [/b][/*][*][b][url=https://www.geogebra.org/m/NjmEPs3t]Proof Challenges[/url]  [/b][/*][/list]
What phenomenon is dynamically being illustrated here? (Vertices are moveable.)
What phenomenon is dynamically being illustrated here? (Vertices are moveable.)
– Tim Brzezinski

Information