Congruence (Vol 1) Over 80 Resources

Tim Brzezinski, Shamashuddin Attar, Mar 27, 2020

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Table of Contents

  1. HSG.CO.A.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. HSG.CO.A.2 - A.5: Experimenting with transformations in the plane
    1. Translations and Rotations
    2. Translating Triangle by a Vector
    3. Translating by Vector: Ex. 16
    4. Reflections
    5. Reflections Introduction
    6. Reflecting About Lines: Ex. 18
    7. Flip Flop Reflection
    8. Footprints in the Sand
    9. Tool for compositions of rigid transformations and dilations
    10. Applet for Multiple Transformations
    11. Messing With Lisa
    12. Rotations: Introduction
    13. Rotating Around Points: Ex. 17
    14. Point Symmetry: Another Perspective
    15. Reflections and Translations
    16. Tessellation by Translation
    17. Parallel Translation
    18. Transformations: Exercise 1
    19. Transformations: Exercise 2
    20. Transformations: Exercise 3
    21. Composing Transformations: Ex. 20
  3. HSG.CO.B.6 - B.8: Understanding 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. Links to Other CCSS High School: Geometry Standards
    1. Geometry Resources
  5. Additional - Links to CCSS High School: Functions Resources
    1. Functions Resources

1.

HSG.CO.A.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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1.31.

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1.33.

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2.

HSG.CO.A.2 - A.5: Experimenting with transformations in the plane

  • 1. Translations and Rotations
  • 2. Translating Triangle by a Vector
  • 3. Translating by Vector: Ex. 16
  • 4. Reflections
  • 5. Reflections Introduction
  • 6. Reflecting About Lines: Ex. 18
  • 7. Flip Flop Reflection
  • 8. Footprints in the Sand
  • 9. Tool for compositions of rigid transformations and dilations
  • 10. Applet for Multiple Transformations
  • 11. Messing With Lisa
  • 12. Rotations: Introduction
  • 13. Rotating Around Points: Ex. 17
  • 14. Point Symmetry: Another Perspective
  • 15. Reflections and Translations
  • 16. Tessellation by Translation
  • 17. Parallel Translation
  • 18. Transformations: Exercise 1
  • 19. Transformations: Exercise 2
  • 20. Transformations: Exercise 3
  • 21. Composing Transformations: Ex. 20

2.1.

Translations and Rotations

Direct Isometries
Translations and rotations are [i]direct isometries[/i]. If you read the names of the vertices in cyclic order (A-B-C and A'-B'-C'), both would be read in the counterclockwise (or clockwise) direction.
Translation
Rotation
– Steve Phelps

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2.19.

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3.

HSG.CO.B.6 - B.8: Understanding 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

3.1.

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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4.

Links to Other CCSS High School: Geometry Standards

  • 1. Geometry Resources

4.1.

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

5.

Additional - Links to CCSS High School: Functions Resources

  • 1. Functions Resources

5.1.

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

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