# Construction Pod Game: Part A

- Author:
- Gerry Stahl

- Topic:
- Geometry

## Welcome to the Construction Pod Game

## LEVEL 1. BEGINNER LEVEL

## Challenge 01: Play House

How can you tell if a new point is placed on a line that is already there? Dragging a point with the arrow tool is called the DRAG TEST in GeoGebra. It is very important way to make sure that you constructed what you thought you were constructing -- to be sure that things are connected properly. Always drag points you create to check them.

If you want to construct a line segment, is it better to place the two end points first and then make the segment go from one to the other, or should you just place the line and let it create its own end points?

If you want to create a circle, should you first create a point for its center and a point on its circumference, of should you just create the circle and let it create its own defining points?

## Challenge 02: Play with Stick People

Which points in the stick woman can move independently? Which points move the whole woman? Which points move parts of the woman?

Why do some points move independently and others always move other points and lines? Can you tell what order the woman was created in? What was the first point, etc.? Can you create a stick woman that moves differently? Use the DRAG TEST to make sure the stick figure is working the way you want it to.

## Challenge 03: Play around with Points, Lines and Circles

How can you make a new point "stick" to an existing line segment? Can that point go off the ends of the line segment?

How can you test to make sure that a point will always stay on a line segment? How can you test to make sure that one line segment always starts on another line segment? How can you test that a circle always has its center along a certain line segment?

In the original construction, which points would you have to drag to test that end F of line segment CF always stays on the circumference of circle DE -- no matter how any other points in the construction are dynamically moved?

## LEVEL 2. CONSTRUCTION LEVEL

## Challenge 04: Play by Dragging Connections

What does each point in this construction control? Are there any points that cannot be dragged (except by dragging a different point)? Do they have different colors? What sequence of construction steps could have been used to build this?

## Challenge 05: Play with Hidden Objects

What is the difference between a Line and a Line Segment? What is the difference between a circle radius, a circle diameter and a circle circumference?

What difference does it make if you hide a line or you delete the line in dynamic geometry?

## Challenge 6. Construct Polygons in Different Ways

What are polygons with 3, 4, 5 and 6 sides called? What differences do you notice about the polygons constructed in these three different ways? Drag all the points around. What stays the same? What does this make you wonder?

## LEVEL 3. TRIANGLE LEVEL

## Challenge 07: Construct an Equilateral Triangle

Did you construct your own equilateral triangle. Did you use the DRAG TEST to make sure it works properly? The equilateral construction opens up the world of geometry; if you understand how it works deeply, you will understand much about geometry. In geometry, a circle is defined as the set of points that are all the same distance from the center point. So every radius of a certain circle is the same length. Drag each point in your triangle and discuss how the position of third point is dependent on the distance between the first two points. Is your triangle equilateral (all sides equal and all angles equal)? Why? How do you know? Does it have to be?

## Challenge 08: Find Dynamic Triangles

What kinds of triangles did you find in the figure? When you dragged the points, did any of the triangles change kind? For instance, can triangle ABF be a right triangle or equilateral? Discuss how this is possible. Are there some kinds of triangles you are not sure about? Why are you sure about some relationships? Does everyone in your pod agree?

## LEVEL 4: CIRCLE LEVEL

## Challenge 09: Construct the Midpoint

Do you think that point E is in the middle of line segment AB? Do you think that point E is in the middle of line segment CD? Do you think your point J is in the middle of line segment FG? Can you prove that any of these are true (without measuring)?

## Challenge 10: Construct a Perpendicular Line

Compare this Challenge with Challenge 9. That construction of the midpoint also constructed a perpendicular. Challenge 10 extended the approach to construct a perpendicular through a point C that was not the midpoint of AB by making a segment DE that has midpoint C. Can you explain why this works? Can you extend the construction in this challenge to work through a point H that is not on line AB at all? Can you explain how your extension works? Does is still work when you drag point H all around?

## Challenge 11: Construct a Parallel Line

Do you see how to use the GeoGebra perpendicular line tool in the toolbar? It constructs something like you did in the last Challenge and hides all the construction lines and circles. Of course, you could also do the construction yourself. Most GeoGebra tools just automate constructions to save you steps. Do you prefer to do the construction yourself just using the elements of geometry: points, lines and circles? Did your new line (HI) stay parallel to your original line (EF) no matter what points you dragged? Explain why a perpendicular to a perpendicular is a parallel line. Imagine riding your bike in a city with a grid of streets. If you make two right turns, you will be riding a street parallel to your original street. Two more right turns (at right angles on the grid) might bring you back to your original street. If a right angle is 90 degrees, how many degrees is two right angles?