Chapter 5: Relationships Within Triangles

Transcription

1 Name: Hour: Chapter 5: Relationships Within Triangles GeoGebra Exploration and Extension Project Due by 11:59 P.M. on 12/22/15 Mr. Kroll

2 GeoGebra Introduction Activity In this tutorial, you will get used to the basics of GeoGebra. First we need to get to GeoGebra and create a profile: 1. Open the Chrome browser. 2. Navigate to 3. Click Sign In in the upper right corner of the screen. 4. Click the google icon to the right of the username box. Sign into google using your school address and password. Allow the website permission to access your google profile, if prompted. 5. All of your constructions that you will do will be accessible by clicking the icon in the upper right and selecting My Profile. Any time you want to begin a new construction, follow these directions: 1. Select the Start GeoGebra option. 2. On the next screen, click Geometry. 3. Right click and uncheck the Axes option to remove the axes. 4. Click the settings icon in the upper right. Select Options, then Labeling then New Points Only. While still in the Options menu, click on Font Size and select 24. You are now ready to begin constructing using GeoGebra For each of the following: Use a straight edge to draw a properly labeled picture of the indicated special line or line segment. You only need to draw one of each type of line/segment. Perpendicular Bisector Angle Bisector Median Altitude

3 STOP!! CHECK YOU WITH MR. KROLL BEFORE CONTINUING! 1. In a new GeoGebra window, create the following: Construction Tutorial a.) Triangle ABC b.) Use the Measurement Tools to find the measures of Angle A, Angle B, and Angle C. c.) Construct the angle bisector of Angle A. d.) Construct the perpendicular bisector of segment AB. e.) Construct the median from Angle B to segment AC. f.) Construct the altitude from Angle A to segment BC. 2. Save your construction. Title your file as Last Name Construction Practice (i.e. Kroll Construction Practice) and switch from Private to Shared. You will save your next four constructions this using this same procedure. DAY ONE CHECKPOINT. YOU SHOULD BE ABOUT HERE BY THE END OF DAY ONE. GO ON IF YOU HAVE TIME

4 DAY TWO POINTS OF CONCURENCY CONSTRUCTIONS Yesterday you got familiar with GeoGebra, and did some basic constructions to practice using its many functions. Today you will make constructions of each of the points of concurrency we learned about in class. (circumcenter, incenter, centroid, and orthocenter). Circumcenter 1. Describe in a few sentences how you would construct the circumcenter of a triangle using the tools you learned about yesterday in GeoGebra. Check in with Mr. Kroll here before going on! 2. Open GeoGebra/a New Window and construct a triangle and its circumcenter. Be sure to create and label the vertices, midpoints, and the circumcenter on your construction. 3. Describe how you can verify that you created the circumcenter using the measurement tools in GeoGebra (i.e. what is the major property of a circumcenter?). 4. Measure the distances you talked about in number three to verify that you indeed created the circumcenter. 5. Now create the circle that is circumscribed around the triangle that has the circumcenter as its center. 6. How does the type of triangle determine the location of the circumcenter?

5 7. Save your construction. Title your file as Last Name Circumcenter (i.e. Kroll Circumcenter) and switch from Private to Shared. You should now have two constructions saved in your profile. You may close this tab and continue on to the next constructions. Incenter 1. Describe in a few sentences how you would construct the incenter of a triangle using the tools you learned about yesterday in GeoGebra. 2. Open GeoGebra/a New Window and construct a triangle and its incenter. Be sure to create and label the vertices and incenter on your construction. Hide the perpendicular lines that are created outside of your triangle. 3. Now create a perpendicular line from the incenter to each side of your triangle. Use the points tool to add points where these perpendicular lines intersect the sides of your triangle. You should now hide the perpendicular lines by right clicking on them and unchecking show object. 4. Next, create a line segment from the incenter to each of the points of intersection. Right click on the segment and choose object properties. Then choose the color tab and change the color of each segment so that all three are the same color. 5. Describe how you can verify that you created the incenter using the measurement tools in GeoGebra (i.e. what is the major property of an incenter?). 6. Measure the distances you talked about in number five to verify that you indeed created the incenter. 7. Now create the circle that fits inside of the triangle that has the incenter as its center.

6 8. How does the type of triangle determine the location of the incenter? 9. Save your construction. Title your file as Last Name Incenter (i.e. Kroll Incenter) and switch from Private to Shared. You should now have three constructions saved in your GeoGebra profile. You may close this tab and continue on to the next constructions. Centroid 1. Describe in a few sentences how you would construct the centroid of a triangle using the tools you learned about the other day in GeoGebra. 2. Open a new window in GeoGebra and construct a triangle and its centroid. Be sure to create and label the vertices, midpoints, and centroid on your construction. 3. Describe how you can verify that you created the centroid using the measurement tools in GeoGebra (Hint: Think segment lengths). 4. Measure the distances you talked about in number three to verify that you indeed created the centroid. Be sure to measure them on all medians!

7 5. How does the type of triangle determine the location of the centroid? 6. Save your construction. Title your file as Last Name Centroid (i.e. Kroll Centroid) and switch from Private to Shared. You should now have four constructions saved in your GeoGebra profile. You may close this tab and continue on to the final construction. Orthocenter 1. Describe in a few sentences how you would construct the orthocenter of a triangle using the tools you learned about the other day in GeoGebra. 2. Open a new window in GeoGebra and construct a triangle and its orthocenter. Be sure to create a point of intersection. 3. How does the type of triangle determine the location of the orthocenter? 4. Save your construction. Title your file as Last Name Orthocenter (i.e. Kroll Orthocenter) and switch from Private to Shared. You should now have all five constructions saved in your GeoGebra profile. You are now ready create a GeoGebra Book containing your constructions to be shared with Mr. Kroll.

8 Creating and Submitting Your GeoGebraBook Once All Five Constructions Completed. 1. On the GeoGebra main page, click the icon in the upper right and select My Profile. 2. You should see all five of your constructions in the Worksheets tab. 3. Click on the Books tab, then choose Create Book on the far right of the screen. 4. Title your book Last Name GeoGebra Project (i.e. Kroll GeoGebra Project). Scroll to the bottom of the page and select Share with Link, then click Save. You now have a GeoGebra Book that you must add all of your constructions to. 5. Select Add Worksheet and choose Existing Worksheet. 6. Choose Add Material for your first construction. 7. Repeat steps five and six for your remaining four constructions. Your GeoGebra Book is now completed and ready to submit for grading. 8. Select View Book in the upper right corner. 9. Next, click the symbol to share your project. 10. Click the Manage Access for Other Users option. 11. Type my address (krolljo@masd.k12.wi.us) into the space provided. Be sure to click Add Users. If you see krolljo listed below, your project has been shared with me. END OF ACTIVITY! CHECK WITH ME TO SEE THAT I HAVE RECEIVED YOUR CONSTRUCTIONS. DO NOT FORGET TO TURN IN THIS PACKET AS WELL!