Class Note for MATH 409 with Professor Martin at KU
Class Note for MATH 409 with Professor Martin at KU
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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Kansas taught by a professor in Fall. Since its upload, it has received 23 views.
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Date Created: 02/06/15
Math 409 Spring 2009 Introduction to Geometer s Sketchpad Tools On the left you will see a menu of an arrow a dot a circle a line the letter A and something mysterious we won7t ever use its for animations On the top you have various menus Making a triangle Highlight the Point tool the dot and put three dots in the sketch areal Go to the Arrow tool and highlight all three dots Under the Construct menu go to Segment The dots will now be connected You re still in the arrow tool drag one of the dots Drag one of the lines Notice how the triangle deforms as you do each of these things A conjecture about triangles Highlight three vertices and in the Measure menu go to angle Do the same for the other two angles In the Measure menu go to Calculate Highlight one of the measures hit then the next hit then the next hit Deform the triangle by dragging What do you think the sum of the angles of a triangle is Constructing an equilateral triangle The task is to make an equilateral triangle that stays equilateral no matter what you drag Open up a new sketch and start by using the Circle tool on the left to make a circle Notice that Sketchpad shows you two dots the center of the circle and a dot actually on the circle Draw another circle centered at the second dot that contains the rst doti You7ll have to be careful to put the mouse exactly on the dot you want to work with Sketchpad will tell you that you7ve got the right dot by circling it in red Put a dot at one of the points where the two circles meet highlight all three dots construct a triangle from those three dots as before Now go to the Measure menu and select Lengthi Now try dragging around the various pieces of the gure and watch what happens to the lengths Hiding things is crucial in Sketchpad constructions Otherwise things get very messy very fast If you want to work with an equilateral triangle but you no longer need the circles you used to construct it you can highlight them with the arrow tool go to the Display menu and and select Hide Objects You also may want to hide things so you canlt accidentally change themi For example when you draw a circle from scratch Sketchpad shows you a point on the circle What happens when you drag it When you make a construction using a circle you can hide this point so you won7t inadvertently change the dimensions of the circle by dragging it Circles Here are some more useful constructions involving circles 1 Draw two points and choose Circle By Center Point from the Construct menu 2 Draw a line segment Highlight it and one of its endpoints Choose Circle By Center Radius 3 Draw three points Highlight all of themi Choose bft Arc Through 3 Points Notice that the order in which you highlight the points matters Do this again so a different point is highlighted as the middle pointi Parallel and perpendicular lines First play with the Line tool to get segments rays and in nite lines when you hold the mouse down you get to choose which one Now make some kind of line make a point off the line highlight both and choose Parallel Line from the Construct menui Again highlight the original line and point and choose Perpendicular Line Tangent lines Make a circle Put a point on the circle either with the Point tool or in the Construct menu We want a line tangent to the circle through the point But there s no instruction for it Ah but we have a theorem 7 which you7ll prove later 7 which says that a tangent to a circle at a point is perpendicular to the diameter at the point So construct the radius between the point and the center of the circle Then construct the perpendicular to the radius through the point Voila Changing appearance Pick any construction you made and use the Display menu to play with changing colors of points and lines and line widthsi Basically you just highlight what you want to change and then change it Naming Go to the Text tool the A on the side menu Experiment with clicking on things to name themi Basically click once and its namedi Click again and the name goes away Click twice very fast and you get to change the labeli You need to be a little careful if a small letter appears Sketchpad thinks youlre naming a line if a capital letter appears it thinks you re naming a point if an appears it thinks youlre naming a circle So you might have to be careful where the cursor appears so you donlt name the wrong thing Troubleshooting Usually when something goes wrong in Sketchpad its because you7ve highlighted too much or too little or just plain the wrong things Sometimes its because you7ve highlighted things in the wrong order erg Circle By Center Point 7 the center has to come rst
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