7.4 Worksheet Symmetry with Geogebra

Transcription

1 7.4 Worksheet Symmetry with Geogebra 1. What is Geogebra? 1 Geogebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package. It has received several educational software awards in Europe and the USA. Today we are going to use Geogebra to explore reflections and symmetry! 2. Setting up Geogebra 1. Go to to start Geogebra. 2. If you receive a warning message, click Run. (See: Figure 1 to the right) 3. Practice Saving your Image Figure 1: Warning Message Before doing anything you should know how to save your project. Practice this by following the steps below. (Figure 2) 1. On your Geogebra window you should see the word File just above all of the buttons. Click on File. 2. A menu will open up. Click on Export. 3. Finally, click on Graphics View as Picture. 4. A window will open asking you to save your file. Click Save. Another window will open asking you to call your file something. Call the file test.png and save it. You should save the file somewhere that you will be able to find it later. Figure 2: How to save your image 4. Get comfortable Take 10 minutes to familiarize yourself with Geogebra. Play around with the tools and try to figure out what they do. Once your are comfortable, you may move on to the next part of the assignment

2 5. Reflection 1. Create a 6-sided polygon using the Polygon Tool. Once you have selected the tool, you can click in 6 different places - which will be aptly named points A, B, C, D, E, F - and then click the first point (A) again. MAKE IT SMALL! 2. The vertices of your polygon should be A, B, C, D, E, F. 3. Draw a line beside your object using the Line through Two Points Tool. Once you select the tool, click in any two places and the line will appear going through them. The two places you ve clicked are now also called points G, H. The line will be the line of reflection. 4. Make a reflection of your polygon through GH using the Reflect Object about Line Tool. You can do this by selecting the tool, clicking on your polygon ABCDEF and finally clicking on your line GH. 5. You should have managed to create a reflected polygon A B C D E F. If it didn t work check with your teacher. RULE #1 The perpendicular bisector is a line that goes through the midpoint of another line at a right angle (90 ). RULE #2 RULE #3 If a perpendicular bisector of the line GH goes through A, it will go through A as well. If A happens to be ON the line of reflection, then A and A are the same point. 6. Lets create some perpendicular bisectors. Select the Perpendicular Line Tool. Click on your point A and then click your line GH. A line that is at a right angle to GH should have appeared which also goes through both A and A. Repeat this for B, C, D, E, F so that you have 6 perpendicular bisectors. 7. At this point, put your hand up so that your teacher can check your work and initial your sheet. 2

3 6. The cool part! 1. Try moving things around to see what happens. Select the Move Tool. 2. Grab the polygon and move it around. What happens to the reflection? (answer the question in the space below) 3. Select one of the vertices (A, B, C, D, E, F ) and move it around. If you select A and move it around, what happens to A? (answer below) 4. Select your line GH and move it around. What happens to the polygon? (seeing a pattern here?) 5. Notice how the perpendicular bisectors always follow the rules listed on the previous page, no matter what you do to ABCDEF or GH! This is awesome? (circle one) A) Yes, this is actually quite amazing. B) Yes, but I m just saying that because I know it s what you want to hear. C) No, this isn t better than video games. (I appreciate your honesty) Save your file! SAVE IT. SAVE IT. SAVE IT. After you ve completed everything, save your workspace using the method on the front page of this worksheet. This time call your file reflection.png. If you need help, ask your teacher. 3

4 7. Lines of Symmetry RULE #4 A line of symmetry is a line of reflection that passes through an object such that the object and its reflection overlap each other flawlessly. If you had a piece of paper and you were able to perfectly fold it in half, the crease left in the paper is a line of symmetry. 1. DELETE EVERYTHING FIRST Create a square using the Regular Polygon Tool. The Regular Polygon Tool is different than the Polygon Tool. Ask your teacher if you can t find it! 2. Create the lines of symmetry using either the Perpendicular Bisector Tool or Line through Two Points Tool. Ask your teacher if you can t find the Perpendicular Bisector Tool! 3. The Perpendicular Bisector Tool will create a perpendicular line in the middle of any side that you click on. You can create two lines of symmetry by using the Perpendicular Bisector Tool on two sides so that it looks like there is an X going through the square. Notice that if you were working with a paper square, you could fold it in half perfectly if the crease were on these lines. 4. The Line through Two Points Tool can create two more lines of symmetry by using it to click on points that are opposite (diagonal) of each other. If your square has points ABCD then the Line through Two Points Tool through AC and BD will give you the lines of symmetry. Again, folding a paper square over on these lines will have the fold overlap flawlessly. 5. There should be 4 lines of symmetry for a square. 6. DELETE EVERYTHING AND START AGAIN Repeat this for a regular 5-sided polygon (pentagon). How many lines of symmetry are there for a pentagon? 7. DELETE EVERYTHING AND START AGAIN Repeat this for a regular 6-sided polygon (hexagon). How many lines of symmetry are there for a hexagon? 8. DELETE EVERYTHING AND START AGAIN Repeat this for a regular 7-sided polygon (heptagon). How many lines of symmetry are there for a heptagon? 9. At this point, put your hand up so that your teacher can check your work and initial your sheet. 10. Save the picture of your heptagon with all of the lines of symmetry. Call it heptagon.png. 11. If you created a regular n-gon (a polygon with n sides, all the same length and angles) how many lines of symmetry would it have? 4

5 8. Done? Nice work. Just a few more things Make sure that you ve answered ALL of the questions on this worksheet. 2. test.png, reflection.png, and heptagon.png to the address specified by your teacher. Include your name and your partner s name(s) in the BONUS: Done early? Create a alien/monster in Geogebra with at least one line of symmetry. (Nightmare Mode: Create one with two or more lines of symmetry). 4. Have a nice day! 2 2 You can request the open source L A TEX file for this worksheet by ing Gabriel Scholz at scholz.gabe@gmail.com Last modified on February 21,