CCSS High School: Geometry (Congruence) Volume 2

Tim Brzezinski, Raman Kullakanda, Nov 25, 2017

[b]This GeoGebra Book contains lots of discovery-based learning activities, investigations, and meaningful remediation worksheets that were designed to help enhance students' learning of geometry concepts both inside and outside of the mathematics classroom. [color=#1551b5]This GeoGebra Book also contains contributions from the following individuals: Steve Phelps ([url]https://www.geogebra.org/stevephelps[/url]) Jennifer Silverman ([url]https://www.geogebra.org/jennifer+silverman[/url]) Without their amazing talent and creativity, this resource would not have been possible. [/b][/color]

Table of Contents

  1. HSG.CO.C.9
    1. Proof Prompt (A)
    2. Animation 128
    3. Proof Prompt (B)
    4. Animation 127
    5. Proof Prompt (C)
    6. Animation 131
    7. Proof Prompt (D)
    8. Animation 130
    9. Vertical Angles Exploration (1)
    10. Vertical Angles Exploration (2)
    11. Vertical Angles Theorem
    12. Animation 1
    13. Transversal Intersects Parallel Lines
    14. Corresponding Angles: Quick Investigation
    15. Congruent Corresponding Angles to Start? (Quick Investigation)
    16. Exploring Corresponding Angles (V2)
    17. Alternate Interior Angles: Quick Investigation
    18. Alternate Interior Angles Theorem (V1)
    19. Exploring Alternate Interior Angles (V2)
    20. Alternate Interior Angles Theorem (V3)
    21. Animation 16
    22. Alternate Exterior Angles: Quick Investigation
    23. Alternate Exterior Angles Theorem (V1)
    24. Exploring Alternate Exterior Angles (V2)
    25. Animation 39
    26. Animation 60
    27. Same-Side-Interior Angles: Quick Investigation
    28. Same Side Interior Angles Theorem
    29. Animation 29
    30. Same-Side-Exterior Angles: Quick Investigation
    31. Exploring Same Side Exterior Angles
    32. Animation 73
    33. Solution to Parallel Lines & Angles Problem
    34. Interesting Coplanar Locations (1)
    35. A Special Theorem: Part 1 (V1)
    36. A Special Theorem: Part 2 (V1)
    37. A Special Theorem: Part 2 (V2)
    38. A Special Theorem: Part 2 (V3)
    39. Animation 57
    40. A Special Theorem: Part 2 (V4)
    41. PBT (Part 1) - Quick
    42. PBT (Part 2) - Quick
    43. Where in This City? (1)
    44. CT Home Depots
    45. Where in NYC? (VA)
    46. Where in NYC? (VB)
    47. Where in NYC? (VC)
    48. Angle Bisector Theorem (Part 1)
    49. Another Special Theorem: Part 1 (V1)
    50. Another Special Theorem: Part 2 (V1)
    51. Another Special Theorem: Part 1 (V2)
    52. Animation 58
    53. Another Special Theorem: Part 1 (V3)
    54. Effortless Trisections
    55. Animation 134
    56. Parallel Lines Congruent Segments Theorem
    57. Parallel Lines Proportionality Theorem
    58. Animation 135
  2. HSG.CO.C.10
    1. Triangle Area Action! (V1)
    2. Triangle Area Action!!! (V2)
    3. Animation 175
    4. Area of a Triangle (Discovery)
    5. 4 Triangles Action!!!
    6. Animation 179
    7. Triangle Angle Theorems
    8. Animation 171
    9. Triangle Angle Theorems (V2)
    10. Animation 2
    11. Triangle Angle Theorems (V3)
    12. Transformation Proof 3
    13. Triangle Angle Sum Theorem
    14. Obvious Corollary
    15. Animation 140
    16. Triangle Exterior Angle
    17. Animation 102
    18. Triangle: Exterior Angles
    19. Quadrilateral: Exterior Angles
    20. Pentagon: Exterior Angles
    21. Polygons: Exterior Angles
    22. Polygons: Exterior Angles - REVAMPED
    23. Exploring Polygon Angles: Triangle through Octagon
    24. Angles of a Right Triangle
    25. Animation 104
    26. Acute Angles of a Right Triangle
    27. Animation 129
    28. Animation 22
    29. Isosceles Triangle Theorem: Discovery Lab
    30. A Special Triangle & Its Properties (I)
    31. Animation 8
    32. Isosceles Triangle Investigation
    33. Converse of IST (V1)
    34. Animation 82
    35. Animation 23
    36. Another Special Triangle and its Properties (II)
    37. Animation 27
    38. Converse of IST (II)
    39. Animation 84
    40. Isosceles Right Triangle: Quick Investigation
    41. Special Right Triangle (I)
    42. Animation 59
    43. Special Right Triangle (II)
    44. Another Special Right Triangle (Guided Discovery)
    45. Animation 42
    46. Special Line through Triangle V1 (Theorem Discovery)
    47. Special Line through Triangle V2 (Theorem Discovery)
    48. Triangle Midsegment Action!
    49. Animation 141
    50. Midsegment of a Triangle
    51. Triangle Inequality: Discovery Lesson
    52. Triangle Side Possibilities? (V2)
    53. Triangle Inequality
    54. Triangle Inequality (II)
    55. Inequalities in 1 Triangle
    56. Points of Concurrency: Investigation
    57. Orthocenter Exploration
    58. Circumcenter (& Questions)
    59. Circumcenter & Circumcircle Action!
    60. Animation 28
    61. Midpoint of HYP
    62. Animation 46
    63. Incenter Exploration (A)
    64. Incenter Exploration (B)
    65. Incenter & Incircle Action!
    66. Animation 17
    67. Triangle Medians: Quick Investigation
    68. Medians Centroid Theorem (Proof without Words)
    69. Medians and Centroid Dance
    70. Animation 25
  3. HSG.CO.C.11
    1. Parallelogram: Area
    2. Animation 202
    3. Parallelogram Construction Template & Discovery Lab
    4. Parallelogram Template (Scaffolded Discovery)
    5. Parallelogram Template
    6. Parallelogram: Theorem 1
    7. Animation 123
    8. Parallelogram: Theorem 2
    9. Animation 124
    10. Parallelogram: Theorem (3)
    11. Animation 125
    12. Parallelograms (I)
    13. Animation 75
    14. Animation 80
    15. Animation 6
    16. What Kind of Quadrilateral is This? (Part 1)
    17. What Kind of Quadrilateral is This? (Part 2)
    18. What Kind of Quadrilateral is This? (Part 3)
    19. What Kind of Quadrilateral is This? (Part 4)
    20. Special Quadrilateral: Theorem 1
    21. Animation 184
    22. Special Quadrilateral: Theorem 2
    23. Animation 185
    24. Special Quadrilateral: Theorem 3
    25. Animation 186
    26. Special Quadrilateral: Theorem 4
    27. Animation 187
    28. Congruent Opposite Sides of a Quadrilateral
    29. Quadrilateral With Opposite Angles Congruent
    30. What Kind of Quad?
    31. Quadrilateral Investigation (I)
    32. Rhombus Action!
    33. Animation 11
    34. Rhombus Template (Scaffolded Discovery)
    35. Rhombus Template with Investigation Questions
    36. Rectangle Action!
    37. Animation 31
    38. Rectangle Template (Scaffolded Investigation)
    39. Rectangle Template with Investigation Questions
    40. Square Action!
    41. Animation 41
    42. Square Template (Scaffolded Investigation)
    43. Square Template with Investigation Questions
    44. Trapezoids: Median Investiagtion
    45. Trapezoid Median (Midsegment) Action!
    46. Animation 67
    47. Trapezoid Median: 2 Discoveries
    48. Isosceles Trapezoid Action!
    49. Animation 64
    50. Animation 35
    51. Isosceles Trapezoid Template (Scaffolded Discovery)
    52. Isosceles Trapezoid Template
    53. Animation 49
    54. Kite Action!
    55. Animation 26
    56. Kite Template: Scaffolded Investigation
    57. Kite Template with Investigation Questions
    58. Quad Midpoints Action!
    59. Animation 52
  4. HSG.CO.D.12
    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. HSG.CO.D.13
    1. Equilateral Triangle Construction Template
    2. Square Construction Template
    3. Regular Hexagon Construction Template
  6. Links to Other CCSS High School: Geometry Standards
    1. Geometry Resources
  7. Additional - Links to CCSS High School: Functions Resources
    1. Functions Resources

1.

HSG.CO.C.9

  • 1. Proof Prompt (A)
  • 2. Animation 128
  • 3. Proof Prompt (B)
  • 4. Animation 127
  • 5. Proof Prompt (C)
  • 6. Animation 131
  • 7. Proof Prompt (D)
  • 8. Animation 130
  • 9. Vertical Angles Exploration (1)
  • 10. Vertical Angles Exploration (2)
  • 11. Vertical Angles Theorem
  • 12. Animation 1
  • 13. Transversal Intersects Parallel Lines
  • 14. Corresponding Angles: Quick Investigation
  • 15. Congruent Corresponding Angles to Start? (Quick Investigation)
  • 16. Exploring Corresponding Angles (V2)
  • 17. Alternate Interior Angles: Quick Investigation
  • 18. Alternate Interior Angles Theorem (V1)
  • 19. Exploring Alternate Interior Angles (V2)
  • 20. Alternate Interior Angles Theorem (V3)
  • 21. Animation 16
  • 22. Alternate Exterior Angles: Quick Investigation
  • 23. Alternate Exterior Angles Theorem (V1)
  • 24. Exploring Alternate Exterior Angles (V2)
  • 25. Animation 39
  • 26. Animation 60
  • 27. Same-Side-Interior Angles: Quick Investigation
  • 28. Same Side Interior Angles Theorem
  • 29. Animation 29
  • 30. Same-Side-Exterior Angles: Quick Investigation
  • 31. Exploring Same Side Exterior Angles
  • 32. Animation 73
  • 33. Solution to Parallel Lines & Angles Problem
  • 34. Interesting Coplanar Locations (1)
  • 35. A Special Theorem: Part 1 (V1)
  • 36. A Special Theorem: Part 2 (V1)
  • 37. A Special Theorem: Part 2 (V2)
  • 38. A Special Theorem: Part 2 (V3)
  • 39. Animation 57
  • 40. A Special Theorem: Part 2 (V4)
  • 41. PBT (Part 1) - Quick
  • 42. PBT (Part 2) - Quick
  • 43. Where in This City? (1)
  • 44. CT Home Depots
  • 45. Where in NYC? (VA)
  • 46. Where in NYC? (VB)
  • 47. Where in NYC? (VC)
  • 48. Angle Bisector Theorem (Part 1)
  • 49. Another Special Theorem: Part 1 (V1)
  • 50. Another Special Theorem: Part 2 (V1)
  • 51. Another Special Theorem: Part 1 (V2)
  • 52. Animation 58
  • 53. Another Special Theorem: Part 1 (V3)
  • 54. Effortless Trisections
  • 55. Animation 134
  • 56. Parallel Lines Congruent Segments Theorem
  • 57. Parallel Lines Proportionality Theorem
  • 58. Animation 135

1.1.

Proof Prompt (A)

[color=#0000ff][b]Theorem: [/b][/color][br][br]If two lines cross to form [color=#9900ff][b]congruent, adjacent angles[/b][/color], then those [b]lines are perpendicular.[/b] [br][br][br]Write a 2-column (or paragraph) proof that formally proves what this applet informally illustrates. [br][i][color=#cc0000]Be sure to set up an appropriate diagram, state what is given, and state what needs to be proven. [br]Then prove it! [/color][/i] [br][br]
Proof Prompt (A)
– Tim Brzezinski

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

1.7.

–

1.8.

–

1.9.

–

1.10.

–

1.11.

–

1.12.

–

1.13.

–

1.14.

–

1.15.

–

1.16.

–

1.17.

–

1.18.

–

1.19.

–

1.20.

–

1.21.

–

1.22.

–

1.23.

–

1.24.

–

1.25.

–

1.26.

–

1.27.

–

1.28.

–

1.29.

–

1.30.

–

1.31.

–

1.32.

–

1.33.

–

1.34.

–

1.35.

–

1.36.

–

1.37.

–

1.38.

–

1.39.

–

1.40.

–

1.41.

–

1.42.

–

1.43.

–

1.44.

–

1.45.

–

1.46.

–

1.47.

–

1.48.

–

1.49.

–

1.50.

–

1.51.

–

1.52.

–

1.53.

–

1.54.

–

1.55.

–

1.56.

–

1.57.

–

1.58.

–

2.

HSG.CO.C.10

  • 1. Triangle Area Action! (V1)
  • 2. Triangle Area Action!!! (V2)
  • 3. Animation 175
  • 4. Area of a Triangle (Discovery)
  • 5. 4 Triangles Action!!!
  • 6. Animation 179
  • 7. Triangle Angle Theorems
  • 8. Animation 171
  • 9. Triangle Angle Theorems (V2)
  • 10. Animation 2
  • 11. Triangle Angle Theorems (V3)
  • 12. Transformation Proof 3
  • 13. Triangle Angle Sum Theorem
  • 14. Obvious Corollary
  • 15. Animation 140
  • 16. Triangle Exterior Angle
  • 17. Animation 102
  • 18. Triangle: Exterior Angles
  • 19. Quadrilateral: Exterior Angles
  • 20. Pentagon: Exterior Angles
  • 21. Polygons: Exterior Angles
  • 22. Polygons: Exterior Angles - REVAMPED
  • 23. Exploring Polygon Angles: Triangle through Octagon
  • 24. Angles of a Right Triangle
  • 25. Animation 104
  • 26. Acute Angles of a Right Triangle
  • 27. Animation 129
  • 28. Animation 22
  • 29. Isosceles Triangle Theorem: Discovery Lab
  • 30. A Special Triangle & Its Properties (I)
  • 31. Animation 8
  • 32. Isosceles Triangle Investigation
  • 33. Converse of IST (V1)
  • 34. Animation 82
  • 35. Animation 23
  • 36. Another Special Triangle and its Properties (II)
  • 37. Animation 27
  • 38. Converse of IST (II)
  • 39. Animation 84
  • 40. Isosceles Right Triangle: Quick Investigation
  • 41. Special Right Triangle (I)
  • 42. Animation 59
  • 43. Special Right Triangle (II)
  • 44. Another Special Right Triangle (Guided Discovery)
  • 45. Animation 42
  • 46. Special Line through Triangle V1 (Theorem Discovery)
  • 47. Special Line through Triangle V2 (Theorem Discovery)
  • 48. Triangle Midsegment Action!
  • 49. Animation 141
  • 50. Midsegment of a Triangle
  • 51. Triangle Inequality: Discovery Lesson
  • 52. Triangle Side Possibilities? (V2)
  • 53. Triangle Inequality
  • 54. Triangle Inequality (II)
  • 55. Inequalities in 1 Triangle
  • 56. Points of Concurrency: Investigation
  • 57. Orthocenter Exploration
  • 58. Circumcenter (& Questions)
  • 59. Circumcenter & Circumcircle Action!
  • 60. Animation 28
  • 61. Midpoint of HYP
  • 62. Animation 46
  • 63. Incenter Exploration (A)
  • 64. Incenter Exploration (B)
  • 65. Incenter & Incircle Action!
  • 66. Animation 17
  • 67. Triangle Medians: Quick Investigation
  • 68. Medians Centroid Theorem (Proof without Words)
  • 69. Medians and Centroid Dance
  • 70. Animation 25

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

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

2.7.

–

2.8.

–

2.9.

–

2.10.

–

2.11.

–

2.12.

–

2.13.

–

2.14.

–

2.15.

–

2.16.

–

2.17.

–

2.18.

–

2.19.

–

2.20.

–

2.21.

–

2.22.

–

2.23.

–

2.24.

–

2.25.

–

2.26.

–

2.27.

–

2.28.

–

2.29.

–

2.30.

–

2.31.

–

2.32.

–

2.33.

–

2.34.

–

2.35.

–

2.36.

–

2.37.

–

2.38.

–

2.39.

–

2.40.

–

2.41.

–

2.42.

–

2.43.

–

2.44.

–

2.45.

–

2.46.

–

2.47.

–

2.48.

–

2.49.

–

2.50.

–

2.51.

–

2.52.

–

2.53.

–

2.54.

–

2.55.

–

2.56.

–

2.57.

–

2.58.

–

2.59.

–

2.60.

–

2.61.

–

2.62.

–

2.63.

–

2.64.

–

2.65.

–

2.66.

–

2.67.

–

2.68.

–

2.69.

–

2.70.

–

3.

HSG.CO.C.11

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

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

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

3.7.

–

3.8.

–

3.9.

–

3.10.

–

3.11.

–

3.12.

–

3.13.

–

3.14.

–

3.15.

–

3.16.

–

3.17.

–

3.18.

–

3.19.

–

3.20.

–

3.21.

–

3.22.

–

3.23.

–

3.24.

–

3.25.

–

3.26.

–

3.27.

–

3.28.

–

3.29.

–

3.30.

–

3.31.

–

3.32.

–

3.33.

–

3.34.

–

3.35.

–

3.36.

–

3.37.

–

3.38.

–

3.39.

–

3.40.

–

3.41.

–

3.42.

–

3.43.

–

3.44.

–

3.45.

–

3.46.

–

3.47.

–

3.48.

–

3.49.

–

3.50.

–

3.51.

–

3.52.

–

3.53.

–

3.54.

–

3.55.

–

3.56.

–

3.57.

–

3.58.

–

3.59.

–

4.

HSG.CO.D.12

  • 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

4.2.

–

4.3.

–

4.4.

–

4.5.

–

4.6.

–

4.7.

–

4.8.

–

4.9.

–

4.10.

–

4.11.

–

4.12.

–

4.13.

–

4.14.

–

4.15.

–

4.16.

–

4.17.

–

4.18.

–

4.19.

–

4.20.

–

4.21.

–

4.22.

–

4.23.

–

4.24.

–

4.25.

–

4.26.

–

4.27.

–

4.28.

–

4.29.

–

4.30.

–

4.31.

–

4.32.

–

4.33.

–

4.34.

–

4.35.

–

4.36.

–

4.37.

–

4.38.

–

4.39.

–

4.40.

–

4.41.

–

4.42.

–

5.

HSG.CO.D.13

  • 1. Equilateral Triangle Construction Template
  • 2. Square Construction Template
  • 3. 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

5.2.

–

5.3.

–

6.

Links to Other CCSS High School: Geometry Standards

  • 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

7.

Additional - Links to CCSS High School: Functions Resources

  • 1. Functions Resources

7.1.

Functions Resources

[list][*][b][url=https://www.geogebra.org/m/k6Dvu9f3]Interpreting Functions[/url][/b][/*][*][b][url=https://www.geogebra.org/m/uTddJKRC]Building Functions[/url][/b][/*][*][b][url=https://www.geogebra.org/m/GMvvpwrm]Linear, Quadratic, and Exponential Functions[/url][/b][/*][*][b][url=https://www.geogebra.org/m/aWuJMDas]Trigonometric Functions[/url][/b][/*][/list]
Half-life function: Quick Exploration. (Large point & slider moveable.)
What does it mean for a function to be odd? (Points moveable.)
– GeoGebra Team, Tim Brzezinski

Information