Task #13: Squaring the sides of triangles
Construct a widget that demonstrates the theorems in Section 9.1 by following the instructions below:
1. Use the Regular Polygon tool to "square" the sides of the triangles. Click two triangle vertices B, then A (in clockwise order) and enter the number "4" to make a square on that side. Notice that the square has been named "poly2" (in the left-hand menu). Repeat this step two more times with the vertex pairs A, C and C, B to make all three squares.
2. Use the area tool to find the area of the largest square. (This square should be on the side AB of the triangle). The area should appear on the screen.
3. Scroll down to the bottom of the menu on the left-hand side, and in the box labeled "Input," type the following text EXACTLY:
sum=poly3+poly4
then hit enter. This will create the sum of the areas of the squares of the other two sides.
4. Make this sum appear on your window with the Text tool. Once you have clicked a place to put your text box, type Sum= then choose "Advanced" and click the GeoGebra symbol (the ellipse). Find "sum" in the list that appears, and click it. The result should be a text equation that looks like Sum= sum, with the lowercase sum in a yellow box. Click "OK."
5. Compare the area "poly2" to "Sum." Is your triangle an acute, right, or obtuse triangle? Move the point C to experiment with how this changes the value of "Sum," and keep comparing this value to "poly2." Can you get the two to equal each other exactly?
6. Answer the question below.
1. Use the Regular Polygon tool to "square" the sides of the triangles. Click two triangle vertices B, then A (in clockwise order) and enter the number "4" to make a square on that side. Notice that the square has been named "poly2" (in the left-hand menu). Repeat this step two more times with the vertex pairs A, C and C, B to make all three squares.
2. Use the area tool to find the area of the largest square. (This square should be on the side AB of the triangle). The area should appear on the screen.
3. Scroll down to the bottom of the menu on the left-hand side, and in the box labeled "Input," type the following text EXACTLY:
sum=poly3+poly4
then hit enter. This will create the sum of the areas of the squares of the other two sides.
4. Make this sum appear on your window with the Text tool. Once you have clicked a place to put your text box, type Sum= then choose "Advanced" and click the GeoGebra symbol (the ellipse). Find "sum" in the list that appears, and click it. The result should be a text equation that looks like Sum= sum, with the lowercase sum in a yellow box. Click "OK."
5. Compare the area "poly2" to "Sum." Is your triangle an acute, right, or obtuse triangle? Move the point C to experiment with how this changes the value of "Sum," and keep comparing this value to "poly2." Can you get the two to equal each other exactly?
6. Answer the question below.In your own words, explain how the widget demonstrates the theorems from Section 9.1. (Note: You can earn up to 5 bonus points on this task by giving an exceptionally in-depth explanation.)