Geometry Spring Semester

Gary Rubinstein, Jan 28, 2019

Table of Contents

  1. Circle Geometry
    1. Chords And Distance From Center
    2. Chords, Central Angles, and Arcs
    3. Thales Theorem
    4. Inscribed Angle Theorem
    5. Two Inscribed Angles
    6. Tangent Perpendicular To Radius
    7. Angle Formed By Tangent And Chord
    8. Angle Formed By Two Chords
    9. Angle Formed By Two Secants
    10. Angle Formed By A Secant And A Tangent
    11. Angle Formed By Two Tangents
    12. Tangent Tangent Segments
    13. Chord Chord Segment
    14. Tangent Secant Segments
    15. Secant Secant Segments
    16. Congruent Chords In Circle
  2. Trigonometry
    1. Intro To Trig Less Special Right Triangles
    2. Area Of Regular Polygon
  3. Coordinate Geometry
    1. Slope Intercept Form
  4. Transformational Geometry
    1. Line Reflection
    2. Translation
    3. Rotation
    4. Dilation
  5. Constructions
    1. Construct Perpendicular Bisector
    2. Construct Perpendicular From Point On Line
    3. Construct Perpendicular From Point Not On Line
    4. Construct Circle Through Three Points
    5. Copy Segment
    6. Construct Triangle With Three Given Sides
    7. Construct Angle Bisector
    8. Construct An Angle Congruent To A Given Angle
    9. Construct A Line Parallel To A Given Line Through A Given Point
    10. Combining Two Squares
    11. Divide Line Segment
    12. Squaring The Rectangle
    13. Centroid
    14. Construct Pentagon
  6. Not Categorized Yet
    1. Visual Proof That The Square Root Of 2 Is Irrational By Infinite Descent
    2. Archimedes Pi
    3. Euclid 12.7
    4. Volume of Sphere Proof
    5. Volume of a Sphere via Cavalieri's Principle
    6. Archimedes Volume of a Sphere
    7. Cone Unrolled
    8. Surface Of Revolution

1.

Circle Geometry

  • 1. Chords And Distance From Center
  • 2. Chords, Central Angles, and Arcs
  • 3. Thales Theorem
  • 4. Inscribed Angle Theorem
  • 5. Two Inscribed Angles
  • 6. Tangent Perpendicular To Radius
  • 7. Angle Formed By Tangent And Chord
  • 8. Angle Formed By Two Chords
  • 9. Angle Formed By Two Secants
  • 10. Angle Formed By A Secant And A Tangent
  • 11. Angle Formed By Two Tangents
  • 12. Tangent Tangent Segments
  • 13. Chord Chord Segment
  • 14. Tangent Secant Segments
  • 15. Secant Secant Segments
  • 16. Congruent Chords In Circle

1.1.

Chords And Distance From Center

– Gary Rubinstein

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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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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1.15.

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1.16.

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2.

Trigonometry

  • 1. Intro To Trig Less Special Right Triangles
  • 2. Area Of Regular Polygon

2.1.

Intro To Trig Less Special Right Triangles

– Gary Rubinstein

2.2.

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3.

Coordinate Geometry

  • 1. Slope Intercept Form

3.1.

Slope Intercept Form

– Gary Rubinstein

4.

Transformational Geometry

  • 1. Line Reflection
  • 2. Translation
  • 3. Rotation
  • 4. Dilation

4.1.

Line Reflection

– Gary Rubinstein

4.2.

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4.3.

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4.4.

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5.

Constructions

  • 1. Construct Perpendicular Bisector
  • 2. Construct Perpendicular From Point On Line
  • 3. Construct Perpendicular From Point Not On Line
  • 4. Construct Circle Through Three Points
  • 5. Copy Segment
  • 6. Construct Triangle With Three Given Sides
  • 7. Construct Angle Bisector
  • 8. Construct An Angle Congruent To A Given Angle
  • 9. Construct A Line Parallel To A Given Line Through A Given Point
  • 10. Combining Two Squares
  • 11. Divide Line Segment
  • 12. Squaring The Rectangle
  • 13. Centroid
  • 14. Construct Pentagon

5.1.

Construct Perpendicular Bisector

– Gary Rubinstein

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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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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6.

Not Categorized Yet

  • 1. Visual Proof That The Square Root Of 2 Is Irrational By Infinite Descent
  • 2. Archimedes Pi
  • 3. Euclid 12.7
  • 4. Volume of Sphere Proof
  • 5. Volume of a Sphere via Cavalieri's Principle
  • 6. Archimedes Volume of a Sphere
  • 7. Cone Unrolled
  • 8. Surface Of Revolution

6.1.

Visual Proof That The Square Root Of 2 Is Irrational By Infinite Descent

– Gary Rubinstein

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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