Funções Trigonométricas

Tim Brzezinski, Antonio Carlos Bastos Sousa, 17. 4. 2020

Obsah

  1. Calculando medidas de arcos e seus radianos
    1. 1 Radiano: Clara Definição
    2. Animação radial
    3. Ilustração do radiano
    4. Animação: Uma borda de radianos
    5. De Graus para Radianos e de Radianos para Graus
    6. Quiz: De Graus para Rad e Rad para Graus
  2. Angles in Standard Position, Coterminal Angles, Trig Ratios
    1. Angles in Standard Position
    2. Animation 176
    3. Angle Orientations (Standard Position)
    4. Animation 180
    5. Animation 181
    6. Angulos Coterminais Interativos!!! tradução incompleta!
    7. Animation 183
    8. Quiz: Sketching Angles in Standard Position
    9. Coterminal Angles: Question Generator
    10. Defining Trigonometric Ratios
    11. Unit Circle and Sine Graph
    12. Unit Circle and Tangent Graph
    13. Unit Circle and Cosine Graph
  3. Trig Functions of Special Angles
    1. Right Triangle Generator for Right Triangle Trigonometry
    2. Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
    3. Evaluating Trig Functions Given a Point on the Terminal Ray
    4. Quiz: Quadrant Logic (Trig)
    5. Trig Quadrant Logic (2)
    6. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
    7. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
    8. Right Triangle Trigonometry: Intro
    9. What Sine, Cosine, Tangent Mean in a Right Triangle
    10. Right Triangle Solver: Formative Assessment
    11. Right Triangle Trig: Solving for Sides (2)
    12. Quiz: Expressing Angles Using Inverse Trigonometric Function
    13. Trig Ratio Estimations (Right Triangle Context)
    14. Trig Ratio Estimations (Quiz: V1)
    15. Trig Ratio Estimations (Quiz: V2)
    16. Isosceles Right Triangle: Quick Investigation
    17. Special Right Triangle (I)
    18. Another Special Right Triangle (Guided Discovery)
    19. Special Right Triangle (II)
    20. 30-60-90 Triangle
    21. Special Right Triangles: Basic Questions
    22. Quiz: Triângulos retângulos com ângulos notáveis (30°,45° e 60°)
    23. Trig Function Values (30 Degrees)
    24. Animation 148
    25. Trig Function Values (45 Degrees)
    26. Animation 146
    27. Trig Function Values (60 Degrees)
    28. Animation 147
    29. Special Angles in Standard Position: Intro (V1)
    30. Special Angles in Standard Position: Intro (V2)
    31. Special Angles in Standard Position: Intro (V2) - Part 2
    32. Animation 177
    33. Animation 178
    34. Special Angles in Standard Position: Intro (V3)
    35. Animation 182
    36. Quiz 1: Funções trigonométricas de ângulos notáveis
    37. Quiz 2: Trigonometric Functions of Special Angles
  4. Even and Odd Functions
    1. Sine and Cosecant Functions (Special Property)
    2. Sine Identity
    3. Animation 150
    4. Cosine and Secant Functions (Special Property)
    5. Cosine Identity
    6. Animation 149
    7. Tangent and Cotangent Functions (Special Property)
    8. Animation 145
    9. Tangent Identity
    10. Animation 151
  5. Representando graficamente e escrevendo Funções trignométricas
    1. Funções Seno e Cosseno no círculo unitário
    2. Sine & Cosine Period Action (1)!
    3. Animation 190
    4. Animation 191
    5. Sine & Cosine Period Action (2)!
    6. Tangent Function Exploration
    7. Tangent Period Action (1)!
    8. Tangent Period Action (2)!
    9. Animation 192
    10. Cotangent Function Exploration
    11. Transforming Sine and Cosine Functions (1): Dynamic Illustrator
    12. Transforming Sine and Cosine Functions (2): Dynamic Illustrator
    13. Transforming the Sine Function (All Transformations)
    14. Graphing Sine & Cosine Functions (II)
    15. Graphing Sine & Cosine Functions (I)
    16. Transformations of a Sinusoid
    17. Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
    18. Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
    19. Sine Function Modeling (y = a sin(x) + d) Quiz
    20. Cosine Function Modeling (y = a cos(x) + d) Quiz
    21. Modeling with Trigonometric Functions
    22. Sine & Cosine Function Modeling: Finding Correct Parameters
    23. Ferris Wheel Action!!!
  6. Inverse Trig Functions
    1. Inverse Relations: Graphs
    2. Sine Function Domain Restriction Options?
    3. Cosine Function Domain Restriction Options?
    4. Tangent Function Domain Restriction Options?
    5. Inverse Trig Functions: Intuitive Explorations
  7. Solving Trig Equations and Modeling
    1. Ferris Wheel (1): Modeling with Trigonometric Functions
    2. Ferris Wheel (2): Modeling with Trigonometric Functions
  8. Proving Trig Identities
    1. New Trig IDs From Similar Right Triangles
    2. New Trig ID's from Similar Right Triangles (V2)
    3. Pythagorean Trigonometric Identity (1)
    4. Trig ID Movie (II)
    5. Trig ID Movie (III)
  9. Proving Advanced Trig Identities
    1. Sine & Cosine of a Sum: Discovery
    2. Trig ID: Geometric Investigation
    3. Tangent of a Sum: Discovery
    4. Tangent of a Difference: Trig Identity Puzzle + Proof!
    5. Cotangent of a Sum: Discovery
    6. Bizzare Trig Identity?
    7. Animation 105
    8. sin(75) & cos(75) activity
  10. Other Functions Resources
    1. Functions Resources
  11. HSG.SRT.A.1, A.1.A, A.1.B
    1. Dilation Introduction: Transformers!
    2. Dilating a Point (Intro)
    3. Dilating a Line: HSG.SRT.A.1.A
    4. Dilating a Segment: HSG.SRT.A.1.B
  12. HSG.SRT.A.2
    1. Similar Figures: Dynamic Illustration
    2. Animation 243
    3. Properties of Dilations
    4. Properties of Dilations (II)
    5. Proving Triangles Similar (1)
    6. Proving Triangles Similar (2)
    7. Proving Triangles Similar (3)
    8. Proving Triangles Similar (4)
  13. HSG.SRT.A.3
    1. Angle -Angle: Triangle Investigation
    2. AA Similarity Theorem
    3. Animation 97
    4. AAA: Similar Quads?
  14. HSG.SRT.B.4 & B.5
    1. SAS ~ Theorem
    2. SSS ~ Theorem (V1)
    3. Animation 63
    4. SSS ~ Theorem (V2)
    5. SSSS: Similar Quads?
    6. Similar Right Triangles (V1)
    7. Similar Right Triangles (V2)
    8. Animation 13
    9. Pythagorean and similar triangles.
    10. Effortless Trisections
    11. Animation 134
    12. Parallel Lines Congruent Segments Theorem
    13. Parallel Lines Proportionality Theorem
    14. Triangle-Angle Bisector Theorem
    15. Animation 81
    16. Proof Without Words
    17. Wordless Pythagorean Theorem based on Translations
    18. Proof Without Words
    19. Proof Without Words
    20. Proof Without Words
    21. Proof Without Words
    22. Proof Without Words
    23. Proof Without Words
    24. Proof Without Words
    25. Proof Without Words
    26. Proof Without Words
  15. HSG.SRT.D.9 & D.10 & D.11
    1. Triangle Investigation
    2. Law of Sines (& Area)
    3. Law of Sines (Illustrated)
    4. Law of Cosines: Discovery
    5. Bearing Illustrator (1)
    6. Direction Angle Illustrator
    7. Bearing Illustrator (2)
    8. Bearings Summary
    9. Bearing: Dynamic Illustration
    10. Bearings: Dynamic Illustrator
  16. Links to Other CCSS High School: Geometry Standards
    1. Geometry Resources

1.

Calculando medidas de arcos e seus radianos

  • 1. 1 Radiano: Clara Definição
  • 2. Animação radial
  • 3. Ilustração do radiano
  • 4. Animação: Uma borda de radianos
  • 5. De Graus para Radianos e de Radianos para Graus
  • 6. Quiz: De Graus para Rad e Rad para Graus

1.1.

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1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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2.

Angles in Standard Position, Coterminal Angles, Trig Ratios

  • 1. Angles in Standard Position
  • 2. Animation 176
  • 3. Angle Orientations (Standard Position)
  • 4. Animation 180
  • 5. Animation 181
  • 6. Angulos Coterminais Interativos!!! tradução incompleta!
  • 7. Animation 183
  • 8. Quiz: Sketching Angles in Standard Position
  • 9. Coterminal Angles: Question Generator
  • 10. Defining Trigonometric Ratios
  • 11. Unit Circle and Sine Graph
  • 12. Unit Circle and Tangent Graph
  • 13. Unit Circle and Cosine Graph

2.1.

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2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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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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3.

Trig Functions of Special Angles

  • 1. Right Triangle Generator for Right Triangle Trigonometry
  • 2. Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
  • 3. Evaluating Trig Functions Given a Point on the Terminal Ray
  • 4. Quiz: Quadrant Logic (Trig)
  • 5. Trig Quadrant Logic (2)
  • 6. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
  • 7. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
  • 8. Right Triangle Trigonometry: Intro
  • 9. What Sine, Cosine, Tangent Mean in a Right Triangle
  • 10. Right Triangle Solver: Formative Assessment
  • 11. Right Triangle Trig: Solving for Sides (2)
  • 12. Quiz: Expressing Angles Using Inverse Trigonometric Function
  • 13. Trig Ratio Estimations (Right Triangle Context)
  • 14. Trig Ratio Estimations (Quiz: V1)
  • 15. Trig Ratio Estimations (Quiz: V2)
  • 16. Isosceles Right Triangle: Quick Investigation
  • 17. Special Right Triangle (I)
  • 18. Another Special Right Triangle (Guided Discovery)
  • 19. Special Right Triangle (II)
  • 20. 30-60-90 Triangle
  • 21. Special Right Triangles: Basic Questions
  • 22. Quiz: Triângulos retângulos com ângulos notáveis (30°,45° e 60°)
  • 23. Trig Function Values (30 Degrees)
  • 24. Animation 148
  • 25. Trig Function Values (45 Degrees)
  • 26. Animation 146
  • 27. Trig Function Values (60 Degrees)
  • 28. Animation 147
  • 29. Special Angles in Standard Position: Intro (V1)
  • 30. Special Angles in Standard Position: Intro (V2)
  • 31. Special Angles in Standard Position: Intro (V2) - Part 2
  • 32. Animation 177
  • 33. Animation 178
  • 34. Special Angles in Standard Position: Intro (V3)
  • 35. Animation 182
  • 36. Quiz 1: Funções trigonométricas de ângulos notáveis
  • 37. Quiz 2: Trigonometric Functions of Special Angles

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3.6.

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3.7.

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3.9.

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3.10.

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3.11.

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3.12.

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3.13.

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3.14.

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3.15.

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3.16.

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3.17.

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3.18.

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3.19.

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3.20.

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3.21.

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3.22.

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3.23.

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3.24.

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3.25.

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3.26.

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3.27.

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3.28.

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3.29.

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3.30.

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3.31.

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3.32.

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3.33.

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3.34.

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3.35.

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3.36.

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3.37.

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4.

Even and Odd Functions

  • 1. Sine and Cosecant Functions (Special Property)
  • 2. Sine Identity
  • 3. Animation 150
  • 4. Cosine and Secant Functions (Special Property)
  • 5. Cosine Identity
  • 6. Animation 149
  • 7. Tangent and Cotangent Functions (Special Property)
  • 8. Animation 145
  • 9. Tangent Identity
  • 10. Animation 151

4.1.

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4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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5.

Representando graficamente e escrevendo Funções trignométricas

  • 1. Funções Seno e Cosseno no círculo unitário
  • 2. Sine & Cosine Period Action (1)!
  • 3. Animation 190
  • 4. Animation 191
  • 5. Sine & Cosine Period Action (2)!
  • 6. Tangent Function Exploration
  • 7. Tangent Period Action (1)!
  • 8. Tangent Period Action (2)!
  • 9. Animation 192
  • 10. Cotangent Function Exploration
  • 11. Transforming Sine and Cosine Functions (1): Dynamic Illustrator
  • 12. Transforming Sine and Cosine Functions (2): Dynamic Illustrator
  • 13. Transforming the Sine Function (All Transformations)
  • 14. Graphing Sine & Cosine Functions (II)
  • 15. Graphing Sine & Cosine Functions (I)
  • 16. Transformations of a Sinusoid
  • 17. Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
  • 18. Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
  • 19. Sine Function Modeling (y = a sin(x) + d) Quiz
  • 20. Cosine Function Modeling (y = a cos(x) + d) Quiz
  • 21. Modeling with Trigonometric Functions
  • 22. Sine & Cosine Function Modeling: Finding Correct Parameters
  • 23. Ferris Wheel Action!!!

5.1.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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5.9.

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5.10.

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5.11.

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5.12.

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5.13.

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5.14.

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5.15.

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5.16.

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5.17.

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5.18.

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5.19.

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5.20.

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5.21.

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5.22.

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5.23.

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6.

Inverse Trig Functions

  • 1. Inverse Relations: Graphs
  • 2. Sine Function Domain Restriction Options?
  • 3. Cosine Function Domain Restriction Options?
  • 4. Tangent Function Domain Restriction Options?
  • 5. Inverse Trig Functions: Intuitive Explorations

6.1.

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6.2.

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6.3.

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6.4.

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6.5.

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7.

Solving Trig Equations and Modeling

  • 1. Ferris Wheel (1): Modeling with Trigonometric Functions
  • 2. Ferris Wheel (2): Modeling with Trigonometric Functions

7.1.

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7.2.

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8.

Proving Trig Identities

  • 1. New Trig IDs From Similar Right Triangles
  • 2. New Trig ID's from Similar Right Triangles (V2)
  • 3. Pythagorean Trigonometric Identity (1)
  • 4. Trig ID Movie (II)
  • 5. Trig ID Movie (III)

8.1.

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8.3.

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8.5.

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9.

Proving Advanced Trig Identities

  • 1. Sine & Cosine of a Sum: Discovery
  • 2. Trig ID: Geometric Investigation
  • 3. Tangent of a Sum: Discovery
  • 4. Tangent of a Difference: Trig Identity Puzzle + Proof!
  • 5. Cotangent of a Sum: Discovery
  • 6. Bizzare Trig Identity?
  • 7. Animation 105
  • 8. sin(75) & cos(75) activity

9.1.

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9.2.

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9.3.

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9.4.

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9.5.

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9.6.

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9.7.

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9.8.

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10.

Other Functions Resources

  • 1. Functions Resources

10.1.

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11.

HSG.SRT.A.1, A.1.A, A.1.B

  • 1. Dilation Introduction: Transformers!
  • 2. Dilating a Point (Intro)
  • 3. Dilating a Line: HSG.SRT.A.1.A
  • 4. Dilating a Segment: HSG.SRT.A.1.B

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11.4.

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12.

HSG.SRT.A.2

  • 1. Similar Figures: Dynamic Illustration
  • 2. Animation 243
  • 3. Properties of Dilations
  • 4. Properties of Dilations (II)
  • 5. Proving Triangles Similar (1)
  • 6. Proving Triangles Similar (2)
  • 7. Proving Triangles Similar (3)
  • 8. Proving Triangles Similar (4)

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13.

HSG.SRT.A.3

  • 1. Angle -Angle: Triangle Investigation
  • 2. AA Similarity Theorem
  • 3. Animation 97
  • 4. AAA: Similar Quads?

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14.

HSG.SRT.B.4 & B.5

  • 1. SAS ~ Theorem
  • 2. SSS ~ Theorem (V1)
  • 3. Animation 63
  • 4. SSS ~ Theorem (V2)
  • 5. SSSS: Similar Quads?
  • 6. Similar Right Triangles (V1)
  • 7. Similar Right Triangles (V2)
  • 8. Animation 13
  • 9. Pythagorean and similar triangles.
  • 10. Effortless Trisections
  • 11. Animation 134
  • 12. Parallel Lines Congruent Segments Theorem
  • 13. Parallel Lines Proportionality Theorem
  • 14. Triangle-Angle Bisector Theorem
  • 15. Animation 81
  • 16. Proof Without Words
  • 17. Wordless Pythagorean Theorem based on Translations
  • 18. Proof Without Words
  • 19. Proof Without Words
  • 20. Proof Without Words
  • 21. Proof Without Words
  • 22. Proof Without Words
  • 23. Proof Without Words
  • 24. Proof Without Words
  • 25. Proof Without Words
  • 26. Proof Without Words

14.1.

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14.2.

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14.3.

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14.4.

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14.5.

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14.6.

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14.7.

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14.8.

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14.9.

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14.10.

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14.11.

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14.12.

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14.13.

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14.14.

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14.15.

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14.16.

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14.17.

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14.18.

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14.19.

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14.20.

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14.21.

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14.22.

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14.23.

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14.24.

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14.25.

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14.26.

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15.

HSG.SRT.D.9 & D.10 & D.11

  • 1. Triangle Investigation
  • 2. Law of Sines (& Area)
  • 3. Law of Sines (Illustrated)
  • 4. Law of Cosines: Discovery
  • 5. Bearing Illustrator (1)
  • 6. Direction Angle Illustrator
  • 7. Bearing Illustrator (2)
  • 8. Bearings Summary
  • 9. Bearing: Dynamic Illustration
  • 10. Bearings: Dynamic Illustrator

15.1.

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15.7.

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15.8.

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15.9.

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15.10.

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16.

Links to Other CCSS High School: Geometry Standards

  • 1. Geometry Resources

16.1.

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Informace