Congruence (Vol 1)

Tim Brzezinski, Sunita Jadhav, Aug 17, 2021

Table of Contents

  1. Geometry Vocabulary Explorations
    1. Congruent Segments: Quick Exploration
    2. Animation 18
    3. Proving Segments Congruent (Exercise)
    4. Congruent Angles: Definition
    5. Animation 36
    6. Proving Angles Congruent (1)
    7. Proving Angles Congruent (2)
    8. Proving Angles Congruent
    9. Midpoint Definition
    10. Animation 56
    11. Segment Bisector Definition
    12. Animation 160
    13. Perpendicular Lines: Quick Intro
    14. Segment Bisectors (Definitions)
    15. Perpendicular Bisector Definition
    16. Perpendicular Bisector Definition
    17. Animation 15
    18. Angle Bisector Definition (I)
    19. Complementary Meaning?
    20. Animation 48
    21. Supplementary Angles (Quick Exploration)
    22. Animation 19
    23. Circle vs. Sphere
    24. Triangle Altitude Illustrator and Definition Writing Prompt
    25. Animation 162
    26. Triangle Median Illustrator & Definition Writing Prompt
    27. Animation 161
    28. Equilateral Action!!!
    29. Animation 165
    30. Equiangular Action!!!
    31. Animation 166
    32. Regular Polygon Action!
    33. Animation 193
  2. Transformations In the Plane
    1. Exploring Transformations
    2. Exploring Translations in the Coordinate Plane
    3. Exploring Translations in the Coordiante Plane
    4. Rotations: Introduction
    5. Exploring Rotations in the Coordinate Plane
    6. Exploring Rotations Around Points
    7. Exploring Line Reflections in the Coordinate Plane (Ver 1)
    8. Exploring Line Reflections
    9. Messing With Lisa
    10. Point Symmetry: Another Perspective
    11. Translations and Rotations
    12. Translating Triangle by a Vector
    13. Tessellation by Translation
    14. Parallel Translation
    15. Reflections
    16. Reflections and Translations
    17. Reflections Introduction
    18. Flip Flop Reflection
    19. Footprints in the Sand
    20. Composing Transformations: Line Reflections and Rotation
    21. Tool for compositions of rigid transformations and dilations
    22. Applet for Multiple Transformations
    23. Transformations: Exercise 1
    24. Transformations: Exercise 2
    25. Transformations: Exercise 3
    26. 90 Degree Rotation about ANY POINT: Quick Exploration
    27. Warm Up (Part 1)
    28. Warm Up (Part 2)
    29. Keep Going (Part 3)
    30. Keep Going (Part 4)
    31. Keep Going (Part 5)
    32. Wrap Up (Part 6)
    33. Extending Beyond (Part 7)
  3. Transformations in Space
    1. Reflecting about Planes
    2. Reflecting about Planes: Introduction
    3. Reflecting about x = 0
    4. Reflecting about y = 0
    5. Reflecting about z = 0
    6. Reflecting about y = x
    7. Reflecting about z = x
    8. Reflecting about z = y
    9. Reflecting about Planes: AR Template
  4. Congruence in Terms of Rigid Motions
    1. Are the triangles congruent (part 2)?
    2. Are the triangles congruent (part 3)?
    3. Congruent Figures: Dynamic Illustration
    4. Animation 242
    5. Proving Tri's Congruent (I)
    6. Proving Tri's Congruent (II)
    7. SAS - Exercise 1A
    8. SAS - Exercise 1B
    9. SAS - Exercise 2
    10. SAS - Exercise 3
    11. SSS: Exercise 1
    12. SSS: Exercise 2
    13. SSS: Exercise 3
    14. SAS: Dynamic Proof!
    15. Animation 136
    16. SSS: Dynamic Proof!
    17. SSS: Dynamically Illustrated
    18. Animation 138
    19. ASA Theorem?
    20. Animation 137
    21. ASA: Exercise
    22. SSA Theorem?
    23. Ambiguous Case (SSA) Illustrator: All Cases
    24. Is "SSA" Legit? What Do You Think?
    25. Exploring SSA
    26. HL: Hypotenuse-Leg Action!
    27. Animation 225
  5. Naming Congruent Triangles with Reasons
    1. Congruent Triangles 1
    2. Congruent Triangles 2
    3. Congruent Triangles 3
    4. Congruent Triangles 4
    5. Congruent Triangles 5
    6. Congruent Triangles 6
    7. Congruent Triangles 7
  6. Other Geometry Resources
    1. Geometry Resources

1.

Geometry Vocabulary Explorations

  • 1. Congruent Segments: Quick Exploration
  • 2. Animation 18
  • 3. Proving Segments Congruent (Exercise)
  • 4. Congruent Angles: Definition
  • 5. Animation 36
  • 6. Proving Angles Congruent (1)
  • 7. Proving Angles Congruent (2)
  • 8. Proving Angles Congruent
  • 9. Midpoint Definition
  • 10. Animation 56
  • 11. Segment Bisector Definition
  • 12. Animation 160
  • 13. Perpendicular Lines: Quick Intro
  • 14. Segment Bisectors (Definitions)
  • 15. Perpendicular Bisector Definition
  • 16. Perpendicular Bisector Definition
  • 17. Animation 15
  • 18. Angle Bisector Definition (I)
  • 19. Complementary Meaning?
  • 20. Animation 48
  • 21. Supplementary Angles (Quick Exploration)
  • 22. Animation 19
  • 23. Circle vs. Sphere
  • 24. Triangle Altitude Illustrator and Definition Writing Prompt
  • 25. Animation 162
  • 26. Triangle Median Illustrator & Definition Writing Prompt
  • 27. Animation 161
  • 28. Equilateral Action!!!
  • 29. Animation 165
  • 30. Equiangular Action!!!
  • 31. Animation 166
  • 32. Regular Polygon Action!
  • 33. Animation 193

1.1.

Congruent Segments: Quick Exploration

[color=#000000]The following app illustrates what it means for segments to be classified as [b]congruent segments.  [br][/b][/color]
Interact with the applet below for a few minutes. Be sure to move the LARGE POINTS around each time before you drag the slider! Then answer the questions that follow.
What transformations have we learned about so far? List them.
What transformations did you observe here while interacting with this app?
What does it mean for segments to be classified as [b]congruent segments[/b]? Explain.
– Tim Brzezinski

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2.

Transformations In the Plane

  • 1. Exploring Transformations
  • 2. Exploring Translations in the Coordinate Plane
  • 3. Exploring Translations in the Coordiante Plane
  • 4. Rotations: Introduction
  • 5. Exploring Rotations in the Coordinate Plane
  • 6. Exploring Rotations Around Points
  • 7. Exploring Line Reflections in the Coordinate Plane (Ver 1)
  • 8. Exploring Line Reflections
  • 9. Messing With Lisa
  • 10. Point Symmetry: Another Perspective
  • 11. Translations and Rotations
  • 12. Translating Triangle by a Vector
  • 13. Tessellation by Translation
  • 14. Parallel Translation
  • 15. Reflections
  • 16. Reflections and Translations
  • 17. Reflections Introduction
  • 18. Flip Flop Reflection
  • 19. Footprints in the Sand
  • 20. Composing Transformations: Line Reflections and Rotation
  • 21. Tool for compositions of rigid transformations and dilations
  • 22. Applet for Multiple Transformations
  • 23. Transformations: Exercise 1
  • 24. Transformations: Exercise 2
  • 25. Transformations: Exercise 3
  • 26. 90 Degree Rotation about ANY POINT: Quick Exploration
  • 27. Warm Up (Part 1)
  • 28. Warm Up (Part 2)
  • 29. Keep Going (Part 3)
  • 30. Keep Going (Part 4)
  • 31. Keep Going (Part 5)
  • 32. Wrap Up (Part 6)
  • 33. Extending Beyond (Part 7)

2.1.

Exploring Transformations

Quick Links:
[b]Isometries:[/b][list][*][url=https://www.geogebra.org/m/axnnavdz]Exploring Translations in the Coordinate Plane[/url][/*][*][url=https://www.geogebra.org/m/qsvphdcv][/url][url=https://www.geogebra.org/m/w6tp6rtf]Exploring Rotations in the Coordinate Plane[/url][/*][*][url=https://www.geogebra.org/m/pkwefkcd]Exploring Line Reflections in the Coordinate Plane[/url][/*][/list][br][b]Non Isometries:[/b][br][list][*][url=https://www.geogebra.org/m/x3fqwmcn]Exploring Dilations (Part 1)[/url][/*][/list]
– Tim Brzezinski

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3.

Transformations in Space

  • 1. Reflecting about Planes
  • 2. Reflecting about Planes: Introduction
  • 3. Reflecting about x = 0
  • 4. Reflecting about y = 0
  • 5. Reflecting about z = 0
  • 6. Reflecting about y = x
  • 7. Reflecting about z = x
  • 8. Reflecting about z = y
  • 9. Reflecting about Planes: AR Template

3.1.

Reflecting about Planes

Quick Links:
[list][*][url=https://www.geogebra.org/m/sdhq6jse]Reflecting about Planes: Introduction[/url][/*][*][url=https://www.geogebra.org/m/kjynzuxh]Reflecting about x = 0[/url][/*][*][url=https://www.geogebra.org/m/jxdbhtfp]Reflecting about y = 0[/url][/*][*][url=https://www.geogebra.org/m/ydfag7mq]Reflecting about z = 0[/url][/*][*][url=https://www.geogebra.org/m/vv9g9uqc]Reflecting about y = x[/url][/*][*][url=https://www.geogebra.org/m/cgfdxznc]Reflecting about z = x[/url][/*][*][url=https://www.geogebra.org/m/qbs8zpu4]Reflecting about z = y[/url][/*][/list][list][*][url=https://www.geogebra.org/m/mmehapmq]GeoGebra Book containing all of the above in one volume[/url][/*][/list]
– Tim Brzezinski

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4.

Congruence in Terms of Rigid Motions

  • 1. Are the triangles congruent (part 2)?
  • 2. Are the triangles congruent (part 3)?
  • 3. Congruent Figures: Dynamic Illustration
  • 4. Animation 242
  • 5. Proving Tri's Congruent (I)
  • 6. Proving Tri's Congruent (II)
  • 7. SAS - Exercise 1A
  • 8. SAS - Exercise 1B
  • 9. SAS - Exercise 2
  • 10. SAS - Exercise 3
  • 11. SSS: Exercise 1
  • 12. SSS: Exercise 2
  • 13. SSS: Exercise 3
  • 14. SAS: Dynamic Proof!
  • 15. Animation 136
  • 16. SSS: Dynamic Proof!
  • 17. SSS: Dynamically Illustrated
  • 18. Animation 138
  • 19. ASA Theorem?
  • 20. Animation 137
  • 21. ASA: Exercise
  • 22. SSA Theorem?
  • 23. Ambiguous Case (SSA) Illustrator: All Cases
  • 24. Is "SSA" Legit? What Do You Think?
  • 25. Exploring SSA
  • 26. HL: Hypotenuse-Leg Action!
  • 27. Animation 225

4.1.

Are the triangles congruent (part 2)?

Use the given measurement tools to establish that the corresponding sides of triangle ABS and [br]triangle A'B'C' are parallel and have equal lengths.[br][br]Use the given transformation tools to establish that triangle ABC is congruent to triangle A'B'C'.
– Steve Phelps

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5.

Naming Congruent Triangles with Reasons

  • 1. Congruent Triangles 1
  • 2. Congruent Triangles 2
  • 3. Congruent Triangles 3
  • 4. Congruent Triangles 4
  • 5. Congruent Triangles 5
  • 6. Congruent Triangles 6
  • 7. Congruent Triangles 7

5.1.

Congruent Triangles 1

Anthony Or. [br]GeoGebra Institute of Hong Kong
– Anthony OR 柯志明

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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