Balanced Algebra 1 & Geometry II (2016-2017)

Tim Brzezinski, 22. 9. 2016

Obsah

  1. Preliminary Topics
    1. Plotting Points: Dynamic Illustrator
    2. Plotting Points (x,y): Quiz
    3. Rant Rant Rant Rant!
  2. Expressions & Equations
    1. Substitution & Evaluating Expressions
    2. Simplifying Linear Expressions
    3. Multiplying Binomials
    4. Linear Equation Generator
  3. Inequalities
    1. Quick Inequality Question Generator
    2. Inequality: Graph Illustrator
    3. Graphing Basic Inequalities: 1 Variable (Quiz)
    4. Linear Inequality Generator (1A)
    5. Linear Inequality Generator (1B)
    6. Linear Inequality Generator (II)
  4. Translating Verbal Expressions
    1. Matching Verbal Statements to Algebraic Statements (V1)
    2. Matching Verbal Statements to Algebraic Statements (V2)
    3. Verbal to Algebraic: Translating
  5. Solving Linear Equations: Application Problems
    1. Application Problems: Solving Linear Equations (1)
    2. Perimeter of a Rectangle: Solving Linear Equations
    3. Application Problems: Solving Linear Equations (3)
    4. Friends and Money: Solving Linear Equations
    5. Modeling Linear Growth (and Systems Introduction)
    6. Application Problems: Solving Linear Equations (5)
  6. Geometric Applications
    1. SAP Problem 1 (Discovery)
    2. SAP - Problem 2
    3. SAP - Problem 3
    4. Midpoint Definition
    5. Segment Bisectors (Definitions)
    6. Rotations: Introduction
    7. AAP - Problem 1 (Discovery)
    8. AAP - Problem 2
    9. AAP - Problem 3
    10. Angle Bisector Definition (I)
    11. Complementary Angles Meaning
    12. Supplementary Angles Meaning
    13. Vertical Angles Exploration (1)
    14. Triangle Angle Theorems
    15. Triangle Angle Sum Theorem
  7. Classifying Polygons
    1. Convex vs. Concave
    2. Equilateral Action!!!
    3. Equiangular Action!!!
    4. Regular Polygon Action!
    5. Regular Polygons: Perimeter & Area
    6. Proof Without Words
  8. Polygon Interior & Exterior Angle Sum Theorems
    1. Triangle Angle Theorems
    2. Triangle Angle Theorems (V2)
    3. Quadrilateral Angle Theorems
    4. Pentagon Angle Theorems
    5. Hexagon Angle Theorems
    6. Heptagon Angle Theorems
    7. Octagon Angle Theorems
  9. Polygon Exterior Angle Sum Theorems (Easier to See)
    1. Exterior Angles of a Triangle
    2. Exterior Angles of a Quadrilateral
    3. Exterior Angles of a Pentagon
    4. Exterior Angles of a Hexagon
    5. Exterior Angles of a Heptagon
    6. Exterior Angles of an Octagon
  10. Distance & Midpoint In the Coordinate Plane
    1. Practice: Pythagorean Theorem (1)
    2. Distance in the Coordinate Plane (With Hints)
    3. Distance in the Coordinate Plane (II)
    4. Rise & Run
  11. Isosceles & Equilateral Triangles
    1. Perpendicular Lines: Quick Intro
    2. Segment Bisector Definition
    3. Perpendicular Bisector Definition
    4. Isosceles Triangle (Properties)
    5. A Special Triangle & Its Properties (I)
    6. Converse of IST (V1)
    7. Another Special Triangle and its Properties (II)
    8. Converse of IST (II)
    9. Equilateral Triangle Construction Template
  12. Perpendicular Bisectors, Angle Bisectors, Medians of Triangles
    1. Distance in the Coordinate Plane (With Hints)
    2. Midpoint and Endpoint Coordinates Action!
    3. Midpoint Coordinates (II)
    4. Segment Bisectors (Definitions)
    5. Perpendicular Bisector Definition
    6. PBT (Part 1) - Quick
    7. PBT (Part 2) - Quick
    8. Animation 57
    9. Where in This City? (1)
    10. Circumcenter (& Questions)
    11. Circumcircle: Construction Exercise (VC)
    12. Where in NYC? (VC)
    13. CT Home Depots
    14. Angle Bisector (Basic Exercise)
    15. Angle Bisector Definition (I)
    16. Angle Bisector Theorem (Part 1)
    17. Another Special Theorem: Part 1 (V3)
    18. Animation 58
    19. Incenter Exploration (B)
    20. Incircle: Construction Exercise (VB)
    21. Triangle Medians: Quick Investigation
    22. Medians and Centroid Dance
  13. Slope
    1. Slope Illustrator
    2. Slope: Intuitive Introduction (II)
    3. Slope of a Line: Roller Coaster
    4. Slope (Quiz) I
    5. Slope (Quiz) II
    6. Rise & Run: V2-Revamp
    7. Finding Slope Given 2 Points: Question Generator
    8. Slope: Alternate Interpretation
  14. Graphing Linear Equations
    1. Relating SLOPE and Y-INTERCEPT to the REAL WORLD
    2. Blueprint Equation of a Line (I)
    3. Equation of a Line: Dynamic Illustrator
    4. Graphing Linear Equations: Question Generator (V1)
    5. Graphing Linear Equations: Question Generator (V3)
    6. Graphing Linear Equations: Question Generator (V2)
  15. Writing Linear Equations
    1. Writing the Equation of a Line (I-VA)
    2. Quiz: Modeling with Linear Functions
    3. Writing the Equation of a Line Given a Slope & Point (V1)
    4. Writing Linear Equations Given 2 Points (y-int = integer)
    5. Quiz: Application Problems - Writing Linear Equations Given 2 Points
    6. Writing the Equation of a Line Given Both Intercepts
  16. Circles & Related Theorems
    1. Circle Terminology
    2. Properties of Tangents Drawn to Circles (B)
    3. Diameters & Chords I (VB)
    4. Where to Sit? (I)
    5. Inscribed Angle Theorem: Take 2!
    6. Inscribed Angle Theorem (V1)
    7. Thales' Theorem (VB)
    8. Cyclic Quadrilaterals (IAT: Corollary 3)
  17. Right Triangle Trigonometry
    1. Identifying Sides of Right Triangles
    2. Right Triangle Trigonometry: Intro
    3. True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
    4. What "CO" in COsine Means

1.

Preliminary Topics

  • 1. Plotting Points: Dynamic Illustrator
  • 2. Plotting Points (x,y): Quiz
  • 3. Rant Rant Rant Rant!

1.1.

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1.2.

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1.3.

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2.

Expressions & Equations

  • 1. Substitution & Evaluating Expressions
  • 2. Simplifying Linear Expressions
  • 3. Multiplying Binomials
  • 4. Linear Equation Generator

2.1.

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2.2.

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2.3.

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2.4.

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3.

Inequalities

  • 1. Quick Inequality Question Generator
  • 2. Inequality: Graph Illustrator
  • 3. Graphing Basic Inequalities: 1 Variable (Quiz)
  • 4. Linear Inequality Generator (1A)
  • 5. Linear Inequality Generator (1B)
  • 6. Linear Inequality Generator (II)

3.1.

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3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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4.

Translating Verbal Expressions

  • 1. Matching Verbal Statements to Algebraic Statements (V1)
  • 2. Matching Verbal Statements to Algebraic Statements (V2)
  • 3. Verbal to Algebraic: Translating

4.1.

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4.2.

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4.3.

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5.

Solving Linear Equations: Application Problems

  • 1. Application Problems: Solving Linear Equations (1)
  • 2. Perimeter of a Rectangle: Solving Linear Equations
  • 3. Application Problems: Solving Linear Equations (3)
  • 4. Friends and Money: Solving Linear Equations
  • 5. Modeling Linear Growth (and Systems Introduction)
  • 6. Application Problems: Solving Linear Equations (5)

5.1.

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5.2.

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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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6.

Geometric Applications

  • 1. SAP Problem 1 (Discovery)
  • 2. SAP - Problem 2
  • 3. SAP - Problem 3
  • 4. Midpoint Definition
  • 5. Segment Bisectors (Definitions)
  • 6. Rotations: Introduction
  • 7. AAP - Problem 1 (Discovery)
  • 8. AAP - Problem 2
  • 9. AAP - Problem 3
  • 10. Angle Bisector Definition (I)
  • 11. Complementary Angles Meaning
  • 12. Supplementary Angles Meaning
  • 13. Vertical Angles Exploration (1)
  • 14. Triangle Angle Theorems
  • 15. Triangle Angle Sum Theorem

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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6.6.

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6.7.

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6.8.

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6.9.

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6.10.

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6.11.

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6.12.

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6.13.

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6.14.

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6.15.

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7.

Classifying Polygons

  • 1. Convex vs. Concave
  • 2. Equilateral Action!!!
  • 3. Equiangular Action!!!
  • 4. Regular Polygon Action!
  • 5. Regular Polygons: Perimeter & Area
  • 6. Proof Without Words

7.1.

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7.2.

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7.3.

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7.4.

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7.5.

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7.6.

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8.

Polygon Interior & Exterior Angle Sum Theorems

  • 1. Triangle Angle Theorems
  • 2. Triangle Angle Theorems (V2)
  • 3. Quadrilateral Angle Theorems
  • 4. Pentagon Angle Theorems
  • 5. Hexagon Angle Theorems
  • 6. Heptagon Angle Theorems
  • 7. Octagon Angle Theorems

8.1.

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8.2.

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8.3.

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8.4.

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8.5.

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8.6.

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8.7.

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9.

Polygon Exterior Angle Sum Theorems (Easier to See)

  • 1. Exterior Angles of a Triangle
  • 2. Exterior Angles of a Quadrilateral
  • 3. Exterior Angles of a Pentagon
  • 4. Exterior Angles of a Hexagon
  • 5. Exterior Angles of a Heptagon
  • 6. Exterior Angles of an Octagon

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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10.

Distance & Midpoint In the Coordinate Plane

  • 1. Practice: Pythagorean Theorem (1)
  • 2. Distance in the Coordinate Plane (With Hints)
  • 3. Distance in the Coordinate Plane (II)
  • 4. Rise & Run

10.1.

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10.2.

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10.3.

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10.4.

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11.

Isosceles & Equilateral Triangles

  • 1. Perpendicular Lines: Quick Intro
  • 2. Segment Bisector Definition
  • 3. Perpendicular Bisector Definition
  • 4. Isosceles Triangle (Properties)
  • 5. A Special Triangle & Its Properties (I)
  • 6. Converse of IST (V1)
  • 7. Another Special Triangle and its Properties (II)
  • 8. Converse of IST (II)
  • 9. Equilateral Triangle Construction Template

11.1.

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11.2.

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11.3.

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11.4.

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11.5.

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11.6.

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11.7.

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11.8.

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11.9.

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12.

Perpendicular Bisectors, Angle Bisectors, Medians of Triangles

  • 1. Distance in the Coordinate Plane (With Hints)
  • 2. Midpoint and Endpoint Coordinates Action!
  • 3. Midpoint Coordinates (II)
  • 4. Segment Bisectors (Definitions)
  • 5. Perpendicular Bisector Definition
  • 6. PBT (Part 1) - Quick
  • 7. PBT (Part 2) - Quick
  • 8. Animation 57
  • 9. Where in This City? (1)
  • 10. Circumcenter (& Questions)
  • 11. Circumcircle: Construction Exercise (VC)
  • 12. Where in NYC? (VC)
  • 13. CT Home Depots
  • 14. Angle Bisector (Basic Exercise)
  • 15. Angle Bisector Definition (I)
  • 16. Angle Bisector Theorem (Part 1)
  • 17. Another Special Theorem: Part 1 (V3)
  • 18. Animation 58
  • 19. Incenter Exploration (B)
  • 20. Incircle: Construction Exercise (VB)
  • 21. Triangle Medians: Quick Investigation
  • 22. Medians and Centroid Dance

12.1.

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12.2.

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12.3.

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12.4.

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12.5.

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12.6.

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12.7.

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12.8.

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12.9.

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12.10.

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12.11.

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12.12.

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12.13.

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12.14.

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12.15.

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12.16.

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12.17.

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12.18.

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12.19.

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12.20.

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12.21.

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12.22.

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13.

Slope

  • 1. Slope Illustrator
  • 2. Slope: Intuitive Introduction (II)
  • 3. Slope of a Line: Roller Coaster
  • 4. Slope (Quiz) I
  • 5. Slope (Quiz) II
  • 6. Rise & Run: V2-Revamp
  • 7. Finding Slope Given 2 Points: Question Generator
  • 8. Slope: Alternate Interpretation

13.1.

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13.2.

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13.3.

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13.4.

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13.5.

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13.6.

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13.7.

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13.8.

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14.

Graphing Linear Equations

  • 1. Relating SLOPE and Y-INTERCEPT to the REAL WORLD
  • 2. Blueprint Equation of a Line (I)
  • 3. Equation of a Line: Dynamic Illustrator
  • 4. Graphing Linear Equations: Question Generator (V1)
  • 5. Graphing Linear Equations: Question Generator (V3)
  • 6. Graphing Linear Equations: Question Generator (V2)

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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15.

Writing Linear Equations

  • 1. Writing the Equation of a Line (I-VA)
  • 2. Quiz: Modeling with Linear Functions
  • 3. Writing the Equation of a Line Given a Slope & Point (V1)
  • 4. Writing Linear Equations Given 2 Points (y-int = integer)
  • 5. Quiz: Application Problems - Writing Linear Equations Given 2 Points
  • 6. Writing the Equation of a Line Given Both Intercepts

15.1.

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15.2.

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15.3.

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15.4.

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15.5.

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15.6.

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16.

Circles & Related Theorems

  • 1. Circle Terminology
  • 2. Properties of Tangents Drawn to Circles (B)
  • 3. Diameters & Chords I (VB)
  • 4. Where to Sit? (I)
  • 5. Inscribed Angle Theorem: Take 2!
  • 6. Inscribed Angle Theorem (V1)
  • 7. Thales' Theorem (VB)
  • 8. Cyclic Quadrilaterals (IAT: Corollary 3)

16.1.

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16.2.

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16.3.

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16.4.

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16.5.

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16.6.

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16.7.

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16.8.

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17.

Right Triangle Trigonometry

  • 1. Identifying Sides of Right Triangles
  • 2. Right Triangle Trigonometry: Intro
  • 3. True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
  • 4. What "CO" in COsine Means

17.1.

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17.2.

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17.3.

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17.4.

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Informace