Geometry Fall

Gary Rubinstein, 16.09.2025

Inhaltsverzeichnis

  1. Constructions
    1. Construct An Equilateral Triangle
    2. Copy A Line Segment With A Collapsible Compass
    3. Construct An Angle Bisector
    4. Construct A Midpoint / Perpendicular Bisector
    5. Create A Triangle From Three Given Sides
    6. Perpendicular To A Line Through A Point On The Line
    7. Perpendicular To A Line Through A Point Not On The Line
    8. Copy An Angle
    9. Make Parallel Line
    10. I. 35
    11. I. 41
    12. I. 42
    13. Book I.43
    14. I. 44
    15. Construction I. 35
    16. Construction I. 42
    17. Construction I. 44
    18. Copy of Euclid Book I 47
    19. Congruent Triangles 6
    20. SAS: Dynamic Proof!
    21. pentagon
    22. Construct Regular Pentagon Euclid IV 10
    23. SSS
    24. Circle through 3 points IV. 5
    25. Construct perpendicular through point on line
    26. Construct perpendicular through point not on line
    27. Copy Angle
    28. Make parallel line with copy angle
    29. Line through given point parallel to given line with two perpendiculars
    30. Exterior Angle Inequality
    31. Mystery Quadrilaterals
    32. Isosceles Trapezoid
    33. Pythagorean Theorem Lesson 3
  2. Proofs Before Triangles
    1. Complimentary and Supplementary Angles
    2. Complementary and Supplementary Angles
    3. Complementary and Supplementary Angles
    4. Vertical Angles Theorem: Algebra Proof
    5. Vertical Angles Theorem
    6. Vertical Angles and Linear Pairs
    7. Midpoint
    8. Angle Bisector
    9. Angle and Segment Bisectors
  3. Congruent Triangles
    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
    8. Kala - Exploring Congruent Triangles
    9. Congruent Triangles
    10. SSS Triangle Exploration
    11. SAS: Dynamic Proof!
    12. Animation 136
    13. Copy of Kala - Exploring Congruent Triangles
    14. Kala - Exploring Congruent Triangles SSS ASA SAS SSA
    15. SAS
    16. ASA
    17. Congruent Triangles SSS
    18. SSS
  4. Isosceles Triangle Properties
    1. Altitude and Median
    2. Circumcenter
    3. Graph the Line
  5. Parallel Lines Cut By A Transversal
    1. Transversal Intersects Parallel Lines
  6. Inequalitites
    1. Exterior Angle Inequality
    2. Triangle Side Angle Inequality
    3. Triangle Inequality
  7. Quadrilaterals
    1. Quadrilateral Classification Activity
    2. Quadrilateral Match
    3. Mystery Quadrilaterals
    4. Special Quadrilaterals
    5. Properties of parallelogram
    6. Four Parallelogram Properties
    7. Measurements In Parallelogram
    8. Isosceles Trapezoid
    9. Midsegment and proof
    10. Varignon's Theorem
  8. Area
    1. Euclid I. 35
    2. Euclid I. 41
    3. Euclid Book I 47
    4. I 47 Diagram
  9. Pythagorean Theorem
    1. Pythagorean Theorem Lesson I
    2. Pythagorean Theorem Lesson 2
    3. Pythagorean Theorem Lesson 3
    4. Behold with better colors
    5. Liu Hui Pythagorean Theorem
    6. Pythagorean Theorem using sliders
    7. Perigal Pythagoras With Dilations And Vectors
    8. Shear Pythagoras
    9. Proof Without Words
    10. Proof Without Words
  10. Similar Triangles
    1. Midsegment Generalization

1.

Constructions

  • 1. Construct An Equilateral Triangle
  • 2. Copy A Line Segment With A Collapsible Compass
  • 3. Construct An Angle Bisector
  • 4. Construct A Midpoint / Perpendicular Bisector
  • 5. Create A Triangle From Three Given Sides
  • 6. Perpendicular To A Line Through A Point On The Line
  • 7. Perpendicular To A Line Through A Point Not On The Line
  • 8. Copy An Angle
  • 9. Make Parallel Line
  • 10. I. 35
  • 11. I. 41
  • 12. I. 42
  • 13. Book I.43
  • 14. I. 44
  • 15. Construction I. 35
  • 16. Construction I. 42
  • 17. Construction I. 44
  • 18. Copy of Euclid Book I 47
  • 19. Congruent Triangles 6
  • 20. SAS: Dynamic Proof!
  • 21. pentagon
  • 22. Construct Regular Pentagon Euclid IV 10
  • 23. SSS
  • 24. Circle through 3 points IV. 5
  • 25. Construct perpendicular through point on line
  • 26. Construct perpendicular through point not on line
  • 27. Copy Angle
  • 28. Make parallel line with copy angle
  • 29. Line through given point parallel to given line with two perpendiculars
  • 30. Exterior Angle Inequality
  • 31. Mystery Quadrilaterals
  • 32. Isosceles Trapezoid
  • 33. Pythagorean Theorem Lesson 3

1.1.

Construct An Equilateral Triangle

Euclid I.1
Use the tools to create an equilateral triangle with AB as one of the sides
– Gary Rubinstein

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1.11.

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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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1.17.

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1.18.

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1.19.

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1.20.

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1.21.

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1.22.

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1.23.

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1.24.

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1.25.

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1.26.

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1.27.

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1.28.

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1.29.

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1.30.

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1.31.

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1.32.

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1.33.

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2.

Proofs Before Triangles

  • 1. Complimentary and Supplementary Angles
  • 2. Complementary and Supplementary Angles
  • 3. Complementary and Supplementary Angles
  • 4. Vertical Angles Theorem: Algebra Proof
  • 5. Vertical Angles Theorem
  • 6. Vertical Angles and Linear Pairs
  • 7. Midpoint
  • 8. Angle Bisector
  • 9. Angle and Segment Bisectors

2.1.

Complimentary and Supplementary Angles

Drag the points and change the angles.
Complimentary and Supplementary Angles
– Tony Walsh

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3.

Congruent Triangles

  • 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
  • 8. Kala - Exploring Congruent Triangles
  • 9. Congruent Triangles
  • 10. SSS Triangle Exploration
  • 11. SAS: Dynamic Proof!
  • 12. Animation 136
  • 13. Copy of Kala - Exploring Congruent Triangles
  • 14. Kala - Exploring Congruent Triangles SSS ASA SAS SSA
  • 15. SAS
  • 16. ASA
  • 17. Congruent Triangles SSS
  • 18. SSS

3.1.

Congruent Triangles 1

Anthony Or. [br]GeoGebra Institute of Hong Kong
– Anthony OR ęŸÆåæ—ę˜Ž

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3.6.

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3.7.

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3.8.

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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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3.18.

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4.

Isosceles Triangle Properties

  • 1. Altitude and Median
  • 2. Circumcenter
  • 3. Graph the Line

4.1.

Altitude and Median

– Gary Rubinstein

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5.

Parallel Lines Cut By A Transversal

  • 1. Transversal Intersects Parallel Lines

5.1.

Transversal Intersects Parallel Lines

[b][color=#980000]Students:[/color][/b][br][br]Use the GeoGebra applet above to help you complete the [b][color=#1e84cc]Transversals, Lines, & Related Angles[/color][/b] investigation given to you at the beginning of class.
– Tim Brzezinski

6.

Inequalitites

  • 1. Exterior Angle Inequality
  • 2. Triangle Side Angle Inequality
  • 3. Triangle Inequality

6.1.

– Gary Rubinstein

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7.

Quadrilaterals

  • 1. Quadrilateral Classification Activity
  • 2. Quadrilateral Match
  • 3. Mystery Quadrilaterals
  • 4. Special Quadrilaterals
  • 5. Properties of parallelogram
  • 6. Four Parallelogram Properties
  • 7. Measurements In Parallelogram
  • 8. Isosceles Trapezoid
  • 9. Midsegment and proof
  • 10. Varignon's Theorem

7.1.

Quadrilateral Classification Activity

Investigate the diagonal segments of each quadrilateral by observing how each measurement changes when each of the vertices are moved.
Investigate the diagonal segments of each quadrilateral by observing [b]how[/b] each measurement changes when each of the vertices are moved.
– Robert D Webber

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8.

Area

  • 1. Euclid I. 35
  • 2. Euclid I. 41
  • 3. Euclid Book I 47
  • 4. I 47 Diagram

8.1.

Euclid I. 35

What seems to be true about the red and blue parallelograms? Move the points around and see if this remains true.
– Gary Rubinstein

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9.

Pythagorean Theorem

  • 1. Pythagorean Theorem Lesson I
  • 2. Pythagorean Theorem Lesson 2
  • 3. Pythagorean Theorem Lesson 3
  • 4. Behold with better colors
  • 5. Liu Hui Pythagorean Theorem
  • 6. Pythagorean Theorem using sliders
  • 7. Perigal Pythagoras With Dilations And Vectors
  • 8. Shear Pythagoras
  • 9. Proof Without Words
  • 10. Proof Without Words

9.1.

Pythagorean Theorem Lesson I

– Gary Rubinstein

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9.6.

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9.7.

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9.8.

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9.9.

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9.10.

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10.

Similar Triangles

  • 1. Midsegment Generalization

10.1.

Midsegment Generalization

– Gary Rubinstein

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