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______JAVA MAGE AND MATHMOL
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Tutorial 2:

TUTORIAL 2: THE GEOMETRY OF 2-DIMENSIONS

When the graphics box is appears you will see a graph containing 100 points and labels for the x and y-axis. This tutorial will demonstrate how Kinemage can be used to measure distances and angles on a graph.

Try clicking any point. Notice that the lower left shows the (x,y) coordinate for the point. The lower right side of the screen gives the distance between the last two consecutive points clicked (be sure you are exactly on the point when you do this). Try clicking several points to demonstrate this principle. Notice that clicking the same point twice will leave the same coordinates but change the distance value to 0.

Click on the angle box found at the right side of the screen. An acute angle <ABC will appear.

**Estimate the value of the angle from your knowledge of geometry. <ABC=_________.

To make the activity easier you might want to open another window that contains just the text, or you might want to make a hardcopy by printing the text page. The text for tutorial 2 is available here.

 
Drag mouse in screen to -xy rotation, start near top for z
 

To measure the angle using Kinemage, go to the Other pulldown, click on Measure. Now click point A, then point B and last point C. The lower right will give the angle.

**What is the measure of <ABC using Kinemage? ______.
Is the value in close agreement with your approximation?_______.

The distance shown at the lower right will be the distance between the last two points clicked. Do not be concerned about the
"dhr" value, we will demonstrate this in Tutorial III. To turn off the measure option, go back to the Other pulldown and simply click off Measure --the white lines that were traced over the angle will
be removed.

Remove the green angle from the screen by clicking off the X from the box named angle, at the right side of the screen. Click on
rectangle.

**Estimate the perimeter of the rectangle by counting squares.
What is your estimate of the rectangle? ______

**Measure the perimeter by measuring the distance of each of the line segments in the rectangle using Kinemage. What is your answer?________

**From your knowledge of rectangles, what should each of the angles of a rectangle be equal to?________

**Using Kinemage what values do you get for each angle?____. The
sum of the angles of a rectangle is ________.

Clear the screen of the rectangle. Call up the triangle.

**What is your estimates for: <A=______ <B=_______ <C=________

**What is your estimate for the perimeter of triangle ABC?______
**Using Kinemage find <A=______ <B=________ <C=_______ **The perimeter of triangle ABC using Kinemage is: ___________

Some computers have built in calculators which may help when doing computations with decimals. Ask your teacher if your
computer has a built in calculator.

It is possible with Kinemage to draw your own images. First clear the screen of all images, leaving only the points on the screen. Go to the Other pulldown and click on drawline. When the drawline box appears click "ON". NOTE: Make sure the measure command is clicked off or measure lines will also appear. Click two consecutive points and a line will appear. You can continue to draw line segments between any two points. If you wish to erase the last line you drew, simply click eraseline at the right side of the screen. If you have drawn several lines, clicking eraseline will keep erasing lines in order from the last one drawn. If you wish to erase all lines quickly, return to the drawbox command under the Other pulldown menu and click off. This will remove all lines you have drawn.

Activities for Students:

1) Draw your initials using line segments. Measure the distances and angles used to form the letters.

2) Try finding the interior angles of each of the polygons shown. What is the sum of the interior angles of each of the polygons shown?

3)If you are familiar with the Pythagorean theorem a^2+b^2=c^2 find the diagonal of the square and rectangle. Check your answer by measuring the diagonal using Kinemage.

3) Try drawing several angles and polygons and measure their sides and angles.

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