Category: Assignments (Page 2 of 7)

“Simson’s Theorem: A line that contains the feet of three perpendiculars from a point P to the triangle ABC is called a Simson line for triangle ABC. The point P is the pole of the Simson line.” In other words, given a triangle, a point P outside of the triangle, we will be able to construct the perpendiculars from the point P to the sides of the triangle. The feet of the perpendiculars will lie on a line, which we call it Simson line.

Hi, everyone, I hope my worksheet will help you understand the theorem. To be honest to all of you, the actual work  took for me to finish this was not easy. I almost lost all my work when I tried to make some changes of the wording. I even tried to reproduce the worksheet online, but the internet was off when I tried to save. Fortunately, I finished it. Please find the link below and give me some suggestions on this. Thank you very much for your attention. :)))

Recall our sample GeoGebra dynamic worksheet on Ceva’s Theorem. When you open the worksheet, it automatically takes you to slide 25/25 in the slideshow, but you can jump to slide 1 and scroll through them one by one. What you’re seeing is actually the construction of a single dynamic worksheet, one object at a time. (In this case, I think it is extremely helpful to see the dynamic worksheet built up like this, rather than just seeing the end result.)

If you’d like to add this feature to your own dynamic worksheet, all you have to do is turn on the Navigation Bar for Construction Steps.

In the desktop app:

1. Click on the View menu
2. Select Layout
3. Select Preferences – Graphics from the top of the window (the icon is the overlapping green circle and blue triangle)
4. Under Navigation Bar for Construction Steps, select Show (you can include the play button too if you’d like to automate the slideshow)

Then, when you upload your GeoGebra applet to the online GeoGeobra worksheet that you’re constructing, the navigation bar will appear as it does in the Ceva sample linked above.

I hope this helps with your GeoGebra projects. I can’t wait to see them!

Due date: Thursday, October 27, 2:30pm

Individual are assigned below. You may trade topics with a classmate if you wish.

Your assignment is to include the following two items in an OpenLab post:

1. The statement of the theorem/result that you have been assigned, written in , in the body of the post. You may copy this statement word-for-word from the text, or paraphrase it. Either way, it must be complete and precise.
2. A link to a GeoGebra dynamic worksheet (uploaded to GeoGebra Tube) that helps students understand the statement in your post. The dynamic worksheet should be completely self contained. Think of the worksheet as playing the following role: You are teaching a geometry course and will be absent for one class. The lesson for that day is the topic you have been assigned for this project. The substitute teacher assigned to cover your class does not have a background in geometry, so your students will have to learn the topic exclusively from your dynamic worksheet. Your worksheet must take advantage of the benefits GeoGebra has over traditional paper worksheets (for example, you can make use of the drag test).

You may also include extra details either in the body of your post or in the dynamic worksheet, if you think they will be helpful. For example, you may include hints for the proof of your statement (why is the statement true?) or you may include helpful applications. These are optional and should only be included if they help students understand the statement.

Add the category “Project #2: GeoGebra Dynamic Worksheet” to your post.

There are many resources available online for help creating dynamic worksheets. Here’s one. Read Chapter 3 of the Venema text for other helpful tips. As a sample, here is the dynamic worksheet on Ceva’s theorem that we explored in class.

Once again, your classmates will be asked to score your worksheet and offer detailed feedback. This will be similar to the rubric and feedback form for the Desmos mini-project. Details will be announced later.

Topic assignments:

• JODEL: The theorem of Menelaus (Venema Chapter 9)
• MEI: Simpson’s theorem (Venema 11.6)
• MAJID: Ptolemy’s theorem (Venema 11.7)
• JOSIEL: Napoleon’s theorem and the Napoleon point (Venema 12.1)
• GARY: Morley’s theorem (Venema 12.6)
• SONAM: Circumscribed circle and circumcenter (Venema 4.1)
• EVE: Extended law of sines (Venema 4.1)
• TYNIQUA: Angle bisector concurrence theorem (Venema 4.2)
• LUIS: The medial triangle (Venema Exercises 5.1.1 to 5.1.4)
• ARMANDO: Desargue’s theorem (Venema 11.2)
• JOSUE: TBA