Chapter 5: Relationships Within Triangles

Transcription

1 Name: Hour: Chapter 5: Relationships Within Triangles GeoGebra Exploration and Extension Project Mr. Kroll

2 GeoGebra Introduction Activity In this tutorial, you will get used to the basics of GeoGebra. First we need to load the GeoGebra app onto our Chromebooks by doing the following: 1. Open the Chrome browser. 2. Click on Web Store in the bottom right of the window 3. In the search box in the upper left corner of the window type GeoGebra to search for it in the chrome web store. 4. Click the blue box with a + free on it, then click add in the dialogue box to confirm. 5. GeoGebra is now in your app menu, click on it to run the app! 1. Let s get rid of the coordinate axes. We are going to do a geometric construction, not an algebraic one, so we don t need those. Right click (touch the mouse pad with two fingers) anywhere on the main screen and un-check the axes box. 2. Take a few minutes to construct some geometric figures and play around with the GeoGebra tools. Think about how I have used them in class. Now, lets complete the GeoGebra tutorial by creating objects we talked about in this chapter. First, answer the following questions. 1. What does a perpendicular bisector look like in a triangle? Sketch a picture with proper geometric markings. 2. What does an angle bisector look like in a triangle? Sketch a picture with proper geometric markings. 3. What does a median look like in a triangle? Sketch a picture with proper geometric markings. 4. What does an altitude look like in a triangle? Sketch a picture with proper geometric markings.

3 STOP!! CHECK YOU ANSWERS ABOVE WITH MR. KROLL BEFORE CONTINUING! Now that you are familiar with the app, complete the following activity. 1. Go to file new and create in a single GeoGebra window the following: 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. g. Make a screen shot of the drawing Open Edit from the top menu bar Select Copy Image this will save your drawing to a new tab. Right click and choose copy from the image in the new tab. Open your google drive in a new tab and click create, then document. Choose File then Rename Name the file Last Name-Hour-A Paste your picture into the Google Document. Size you image so that it is easily readable Click the blue share button in the upper right hand corner. In the Invite people box enter krolljo@masd.k12.wi.us 2. Share your screen shot document with Mr. Kroll at krolljo@masd.k12.wi.us 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 the GeoGebra app, 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. Now open the GeoGebra app and construct a triangle and its circumcenter. Be sure to create and label the vertices and midpoints on your construction. 3. Describe how you can verify that you created the circumcenter using the measurement tools in GeoGebra. 4. Measure the distances you talked about in number 3 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.

5 6. How does the type of triangle determine the location of the circumcenter? 7. Make a screen shot of the drawing Open Edit from the top menu bar Select Copy Image this will save your drawing to a new tab. Right click and choose copy from the image in the new tab. Open your google drive in a new tab and click create, then document. Choose File then Rename Name the file Last Name-Hour-B Paste your picture into the Google Document. Size you image so that it is easily readable Click the blue share button in the upper right hand corner. In the Invite people box enter krolljo@masd.k12.wi.us 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. Now open the GeoGebra app and construct a triangle and its incenter. Be sure to create and label the vertices and incenter on your construction. 3. Now create a perpendicular line from the incenter to each side of your traingle. 4. Use the point tool to create the intersection between each perpendicular line and its side. Label these points! 5. Now hide the three perpendicular lines using the green dots in the algebra window, or right click and uncheck the show object box.

6 6. 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. 7. Describe how you can verify that you created the incenter using the measurement tools in GeoGebra. 8. Measure the distances you talked about in number 7 to verify that you indeed created the incenter. 9. Now create the circle that fits inside of the triangle that has the incenter as its center. 10. How does the type of triangle determine the location of the incenter? 11. Make a screen shot of the drawing Open Edit from the top menu bar Select Copy Image this will save your drawing to a new tab. Right click and choose copy from the image in the new tab. Open your google drive in a new tab and click create, then document. Choose File then Rename Name the file Last Name-Hour-C Paste your picture into the Google Document. Size you image so that it is easily readable Click the blue share button in the upper right hand corner. In the Invite people box enter krolljo@masd.k12.wi.us

7 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. Now open a new window in GeoGebra and construct a triangle and its centroid. Be sure to create and label the vertices and midpoints on your construction. 3. Describe how you can verify that you created the centroid using the measurement tools in GeoGebra (Think segment lengths). 4. Measure the distances you talked about in number 3 to verify that you indeed created the centroid. Be sure to measure them on all medians! 5. How does the type of triangle determine the location of the centroid? 6. Make a screen shot of the drawing i. Open Edit from the top menu bar ii. Select Copy Image this will save your drawing to a new tab. Right click and choose copy from the image in the new tab. iii. Open your google drive in a new tab and click create, then document. iv. Choose File then Rename Name the file Last Name-Hour-D v. Paste your picture into the Google Document. vi. Size you image so that it is easily readable vii. Click the blue share button in the upper right hand corner. In the Invite people box enter krolljo@masd.k12.wi.us

8 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. Now open the a new window in GeoGebra and construct a triangle and its orthocenter. Be sure to create and label the vertices and midpoints on your construction. 3. How does the type of triangle determine the location of the orthocenter? 4. Make a screen shot of the drawing i. Open Edit from the top menu bar ii. Select Copy Image this will save your drawing to a new tab. Right click and choose copy from the image in the new tab. iii. Open your google drive in a new tab and click create, then document. iv. Choose File then Rename Name the file Last Name-Hour-E v. Paste your picture into the Google Document. vi. Size you image so that it is easily readable vii. Click the blue share button in the upper right hand corner. In the Invite people box enter krolljo@masd.k12.wi.us END OF ACTIVITY! MAKE SURE ALL SCREENSHOT DOCUMENTS HAVE BEEN SHARED WITH MR. KROLL, THEN TURN IN THIS PACKET!