The Construction Crew Game

Gerry Stahl, Sep 12, 2014

[b]Welcome to the Construction Crew Game[/b] [b]The Construction Crew Game[/b] is a series of challenges for your team to construct interesting and fun geometric figures. Many of the figures will have hidden features and your team will learn how to design them. So put together your Construction Crew with three, four or five people from anywhere in the world who want to play the game together online. [b]Note:[/b] GeoGebraBooks do not yet support collaboration by a team working together on the same figures and chatting about them online. So you can sit around one computer with your team or you can work on your own and discuss what you are doing with other people. Maybe you can use screen-sharing software or the Virtual Math Teams collaboration environment. The Construction Crew Game consists of several [i]levels[/i] of play, each with a set of [i]challenges[/i] to do together in a special online construction zone. The challenges in the beginning levels do not require any previous knowledge about geometry or skill in working together. Playing the challenges in the order they are given will prepare you with everything you need to know for the more advanced levels. [i]Be creative and have fun[/i]. See if you can invent new ways to do the challenges. Try each challenge at your level until everyone in your crew understands how to meet the challenges. Then move on to the next level. Take your time until everyone has mastered the level. Then agree as a team to go to the next level. Most levels assume that everyone has mastered the previous level. The levels become harder and harder -- see how far your team can go. [i]Enjoy playing, exploring, discussing and constructing[/i]!

Table of Contents

  1. Beginner Level
    1. Welcome to the Construction Zone
    2. Beginner Level
    3. Challenge 02: Play with Stick People
    4. Challenge 03: Play around with Points, Lines and Circles
  2. Construction Level
    1. Challenge 04: Play by Dragging Connections
    2. Challenge 05: Play with Hidden Objects
    3. Challenge 06: Construct Polygons in Different Ways
  3. Triangle Level
    1. Challenge 07: Construct an Equilateral Triangle
    2. Challenge 08: Find Dynamic Triangles
  4. Circle Level
    1. Challenge 09: Construct the Midpoint
    2. Challenge 10: Construct a Perpendicular Line
    3. Challenge 11: Construct a Parallel Line
  5. Dependency Level
    1. Challenge 12: Triangles with Dependencies
    2. Challenge 13: An Isosceles Triangle
    3. Challenge 14: A Right Triangle
    4. Challenge 15: An Isosceles-Right Triangle
  6. Compass Level
    1. Challenge 16: Copy a Length
    2. Challenge 17: Use the Compass Tool
    3. Challenge 18: Make Dependent Segments
    4. Challenge 19: Add Segment Lengths
    5. Challenge 20: Copy vs. Construct a Congruent Triangle
    6. Challenge 21: Construct a Congruent Angle
  7. Congruence Level
    1. Challenge 22: Congruent Sides and Angles of Triangles
    2. Challenge 23: Side-Side-Side (SSS)
    3. Challenge 24: Side-Angle-Side (SAS)
    4. Challenge 25: Angle-Side-Angle (ASA)
    5. Challenge 26: Side-Side-Angle (SSA)
  8. Inscribed Polygon Level
    1. Challenge 27: The Inscribed Triangles Challenge Problem
    2. Challenge 28: The Inscribed Quadrilaterals Problem
    3. Challenge 29: Prove Inscribed Triangles
  9. Transformation Level
    1. Challenge 30: Translate by a Vector
    2. Challenge 31: Reflect About a Line
    3. Challenge 32: Rotate Around a Point
    4. Challenge 33: Combine Transformations
    5. Challenge 34: Create Dynamic Patterns
  10. Quadrilateral Level
    1. Challenge 35: Construct Quadrilaterals with Constraints
    2. Challenge 36: Construct a Rhombus
    3. Challenge 37: Quadrilateral Areas
    4. Challenge 38: Build a Hierarchy of Quadrilaterals
  11. Advanced Geometer Level
    1. Challenge 39: The Centroid of a Triangle
    2. Challenge 40: The Circumcenter of a Triangle
    3. Challenge 41: The Orthocenter of a Triangle
    4. Challenge 42: The Incenter of a Triangle
    5. Challenge 43: The Euler Segment of a Triangle
    6. Challenge 44: The Nine-Point Circle of a Triangle
  12. Problem Solver Level
    1. Challenge 45: Treasure Hunt
    2. Challenge 46: Square and Circle
    3. Challenge 47: Cross an Angle
  13. Expert Level
    1. Challenge 48: How Many Ways Can You Invent?
    2. Challenge 49: Dependencies in the World
    3. Challenge 50: Into the Future

1.

Beginner Level

  • 1. Welcome to the Construction Zone
  • 2. Beginner Level
  • 3. Challenge 02: Play with Stick People
  • 4. Challenge 03: Play around with Points, Lines and Circles

1.1.

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1.2.

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1.3.

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1.4.

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2.

Construction Level

  • 1. Challenge 04: Play by Dragging Connections
  • 2. Challenge 05: Play with Hidden Objects
  • 3. Challenge 06: Construct Polygons in Different Ways

2.1.

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2.2.

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2.3.

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3.

Triangle Level

  • 1. Challenge 07: Construct an Equilateral Triangle
  • 2. Challenge 08: Find Dynamic Triangles

3.1.

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3.2.

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4.

Circle Level

  • 1. Challenge 09: Construct the Midpoint
  • 2. Challenge 10: Construct a Perpendicular Line
  • 3. Challenge 11: Construct a Parallel Line

4.1.

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4.2.

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4.3.

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5.

Dependency Level

  • 1. Challenge 12: Triangles with Dependencies
  • 2. Challenge 13: An Isosceles Triangle
  • 3. Challenge 14: A Right Triangle
  • 4. Challenge 15: An Isosceles-Right Triangle

5.1.

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5.2.

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5.3.

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5.4.

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6.

Compass Level

  • 1. Challenge 16: Copy a Length
  • 2. Challenge 17: Use the Compass Tool
  • 3. Challenge 18: Make Dependent Segments
  • 4. Challenge 19: Add Segment Lengths
  • 5. Challenge 20: Copy vs. Construct a Congruent Triangle
  • 6. Challenge 21: 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.

Congruence Level

  • 1. Challenge 22: Congruent Sides and Angles of Triangles
  • 2. Challenge 23: Side-Side-Side (SSS)
  • 3. Challenge 24: Side-Angle-Side (SAS)
  • 4. Challenge 25: Angle-Side-Angle (ASA)
  • 5. Challenge 26: Side-Side-Angle (SSA)

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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8.

Inscribed Polygon Level

  • 1. Challenge 27: The Inscribed Triangles Challenge Problem
  • 2. Challenge 28: The Inscribed Quadrilaterals Problem
  • 3. Challenge 29: Prove Inscribed Triangles

8.1.

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8.2.

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8.3.

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9.

Transformation Level

  • 1. Challenge 30: Translate by a Vector
  • 2. Challenge 31: Reflect About a Line
  • 3. Challenge 32: Rotate Around a Point
  • 4. Challenge 33: Combine Transformations
  • 5. Challenge 34: 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.

Quadrilateral Level

  • 1. Challenge 35: Construct Quadrilaterals with Constraints
  • 2. Challenge 36: Construct a Rhombus
  • 3. Challenge 37: Quadrilateral Areas
  • 4. Challenge 38: 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 Geometer Level

  • 1. Challenge 39: The Centroid of a Triangle
  • 2. Challenge 40: The Circumcenter of a Triangle
  • 3. Challenge 41: The Orthocenter of a Triangle
  • 4. Challenge 42: The Incenter of a Triangle
  • 5. Challenge 43: The Euler Segment of a Triangle
  • 6. Challenge 44: 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.

Problem Solver Level

  • 1. Challenge 45: Treasure Hunt
  • 2. Challenge 46: Square and Circle
  • 3. Challenge 47: Cross an Angle

12.1.

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12.2.

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12.3.

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13.

Expert Level

  • 1. Challenge 48: How Many Ways Can You Invent?
  • 2. Challenge 49: Dependencies in the World
  • 3. Challenge 50: Into the Future

13.1.

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13.2.

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13.3.

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Information