My first week of trying to use GeoGebra was frustrating. I was having a hard time making shapes that were adjustable and movable, or dynamic. At a basic level, I did not understand the

*dependency*of points in Geogebra. Points can be free (completely movable), semi-dependent (only able to move along the object they are placed upon), and fully dependent (not movable, unless the object(s) they lie on move). I didn't realize that if I placed a point at the intersection of two lines, I wouldn't then be able to move those lines by moving that point. The point needed to come first. In my early attempts at figuring this out, I tried to make a rectangle with adjustable dimensions. I went back and forth between creating rectangles that were entirely rigid, to trying to use four free points and creating a quadrilateral that didn't maintain the properties of a rectangle.

A Google search for how to make a dynamic rectangle in GeoGebra led me to a YouTube video presenting a challenge to do just that. The rectangle in the video was dynamic in three points, that is, three points could be moved and the shape would remain a rectangle. I had imagined that four points could be adjustable, so seeing that only three could move gave some more direction to my attempts, of which there were many. However, I still wasn't able to figure it out until I watched the longer challenge video, which provided a key hint: one diagonal of the rectangle must lie on the diameter of a circle. Then I was able to figure out that the vertices on either end of that diagonal are the only free points on the rectangle. Another vertex needs to lie on the circle, and a right angle is guaranteed at that vertex, according to Thales' Theorem. Here's a link to the rectangle on GeoGebra Tube.

My dynamic rectangle with semicircle shown.A and C are freepoints, B is semi-dependent,and D is fully dependent. |

Working through the rectangle challenge problem helped me to understand how objects and figures behave and relate to each other in GeoGebra, and how to carefully put a sketch together to allow adjustment of certain dimensions or positions. Another thing that I particularly wanted to understand, especially for the sake of creating activities for my students, was how to show different steps in a GeoGebra worksheet.

More Google searches on this topic helped me fumble my way through using

*check boxes*. Several objects on a worksheet can be selected to be shown or hidden when a box is checked or unchecked. Here's a GeoGebra worksheet that I created using check boxes. With the help of Professor John Golden, I learned how to use a*slider*to achieve the same results, but with more control of what is being shown or hidden. With a slider set to integer values,*conditions to show objects*could be assigned in the properties for each part of a drawing, according to the values on the slider. This also made it easier to have objects, like text, appear for only one step, or for several steps, without the need for unchecking a box again.A worksheet with check boxes. |

A worksheet with a slider to show steps. Plus, the rectangle's length and width can be adjusted! |

Being able to use a slider will be key to making worksheets for students to use that contain several different examples. In the near future I am hoping to make a GeoGebra worksheet to help my geometry students discover the four triangle congruence theorems (

*SSS*,*SAS*,*ASA*, and*AAS*). In a similar vein, I think a GeoGebra worksheet could be very helpful for my precalculus students learning about the Law of Sines and the*SSA*case, and when two triangles are possible.
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