Construct Dynamic Geometry Together

Gerry Stahl, Aug 4, 2014

The following activities present a special approach to [b]dynamic geometry[/b], which may be quite different from other approaches to learning geometry. They focus specifically on the core idea of dynamic geometry: how to design the construction of figures with [b]dependencies[/b]. They can help you understand geometry better, whether you already studied geometry, are studying it now or will study it in school later. Chatting about the activities in a small group will help you to think about geometry and problem solving on your own in the future. This GeoGebraBook includes 50 GeoGebra activities, grouped in 13 chapters. Chapters 1 and 13 are for you to work on by yourself. The other chapters are for you to work on with a team of two or three friends. Chapters 2 to 7 provide an introduction to dynamic geometry and should be done by your team in order. The other chapters (8 to 12) are optional, depending on the interests of your team.

Table of Contents

  1. Before You Construct Together
    1. Welcome
    2. Stick Figures
    3. Dynamic Points, Lines and Circles
  2. Construct Dynamic-Geometry Objects
    1. The Drag Test
    2. Dependent Geometric Figures
    3. Constructing Polygons
  3. Construct an Equilateral Triangle
    1. Construct an Equilateral Triangle
    2. Find Dynamic Triangles
  4. Construct Using Circles
    1. Construct the Midpoint
    2. Construct a Perpendicular Line
    3. Construct a Parallel Line
  5. Construct Other Triangles
    1. Triangles with Dependencies
    2. An Isosceles Triangle
    3. A Right Triangle
    4. An Isosceles-Right Triangle
  6. Construct Using the Compass
    1. Copy a Length
    2. Use the Compass Tool
    3. Make Dependent Segments
    4. Add Segment Lengths
    5. Copy vs. Construct a Congruent Triangle
    6. Construct a Congruent Angle
  7. Construct Inscribed Polygons
    1. The Inscribed Triangles Challenge Problem
    2. The Inscribed Quarilaterals Challenge Problem
    3. Prove Inscribed Triangles
  8. Construct Congruent Triangles
    1. Combinations of Sides and Angles of Congruent Triangles
    2. Side-Side-Side (SSS)
    3. Side-Angle-Side (SAS)
    4. Angle-Side-Angle (ASA)
    5. Side-Side-Angle (SSA)
  9. Construct using Transformations
    1. Translate by a Vector
    2. Reflect about a Line
    3. Rotate Around a Point
    4. Combine Transformations
    5. Create Dynamic Patterns
  10. Construct Quadrilaterals
    1. Construct Quadrilaterals with Special Constraints
    2. Construct a Rhombus
    3. Quadrilateral Areas
    4. Build a Hierarchy of Quadrilaterals
  11. Advanced Constructions
    1. The Centroid of a Triangle
    2. The Circumcenter of a Triangle
    3. The Orthocenter of a Triangle
    4. The Incenter of a Triangle
    5. The Euler Segment of a Triangle
    6. The Nine-Point Circle of a Triangle
  12. Solve Construction Problems
    1. Treasure Hunt
    2. Square and Circle
    3. Cross an Angle
  13. Wrap Up
    1. How Many Ways Can You Invent?
    2. Dependencies in the World
    3. Into the Future

1.

Before You Construct Together

  • 1. Welcome
  • 2. Stick Figures
  • 3. Dynamic Points, Lines and Circles

1.1.

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1.2.

–

1.3.

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2.

Construct Dynamic-Geometry Objects

  • 1. The Drag Test
  • 2. Dependent Geometric Figures
  • 3. Constructing Polygons

2.1.

–

2.2.

–

2.3.

–

3.

Construct an Equilateral Triangle

  • 1. Construct an Equilateral Triangle
  • 2. Find Dynamic Triangles

3.1.

–

3.2.

–

4.

Construct Using Circles

  • 1. Construct the Midpoint
  • 2. Construct a Perpendicular Line
  • 3. Construct a Parallel Line

4.1.

–

4.2.

–

4.3.

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5.

Construct Other Triangles

  • 1. Triangles with Dependencies
  • 2. An Isosceles Triangle
  • 3. A Right Triangle
  • 4. An Isosceles-Right Triangle

5.1.

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5.2.

–

5.3.

–

5.4.

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6.

Construct Using the Compass

  • 1. Copy a Length
  • 2. Use the Compass Tool
  • 3. Make Dependent Segments
  • 4. Add Segment Lengths
  • 5. Copy vs. Construct a Congruent Triangle
  • 6. Construct a Congruent Angle

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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7.

Construct Inscribed Polygons

  • 1. The Inscribed Triangles Challenge Problem
  • 2. The Inscribed Quarilaterals Challenge Problem
  • 3. Prove Inscribed Triangles

7.1.

–

7.2.

–

7.3.

–

8.

Construct Congruent Triangles

  • 1. Combinations of Sides and Angles of Congruent Triangles
  • 2. Side-Side-Side (SSS)
  • 3. Side-Angle-Side (SAS)
  • 4. Angle-Side-Angle (ASA)
  • 5. Side-Side-Angle (SSA)

8.1.

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8.2.

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8.3.

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8.4.

–

8.5.

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9.

Construct using Transformations

  • 1. Translate by a Vector
  • 2. Reflect about a Line
  • 3. Rotate Around a Point
  • 4. Combine Transformations
  • 5. Create Dynamic Patterns

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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10.

Construct Quadrilaterals

  • 1. Construct Quadrilaterals with Special Constraints
  • 2. Construct a Rhombus
  • 3. Quadrilateral Areas
  • 4. Build a Hierarchy of Quadrilaterals

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.

Advanced Constructions

  • 1. The Centroid of a Triangle
  • 2. The Circumcenter of a Triangle
  • 3. The Orthocenter of a Triangle
  • 4. The Incenter of a Triangle
  • 5. The Euler Segment of a Triangle
  • 6. The Nine-Point Circle of a Triangle

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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12.

Solve Construction Problems

  • 1. Treasure Hunt
  • 2. Square and Circle
  • 3. Cross an Angle

12.1.

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12.2.

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12.3.

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13.

Wrap Up

  • 1. How Many Ways Can You Invent?
  • 2. Dependencies in the World
  • 3. Into the Future

13.1.

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13.2.

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13.3.

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Information