Пифагорын теорем

1. What is the area of the green square? Show or explain your work.

2. What is the area of the blue square? Show or explain your work.

3. What is the area of the red square? Show or explain your work.

4. Add the areas of the green and blue squares. How does this sum compare to the area of the red square?

5. Move the blue and green sliders to the opposite sides. What do you notice? Make an observation about the areas.

6. You already know that the Pythagorean Theorem states [math]a^2+b^2=c^2[/math] where a and b are the legs of the right triangle, and c is the hypotenuse. In the white triangle given in the center of the diagram above, which sides are a and b? Which side is c?

8. The slider should currently be on "right triangle." Compare the sum of the areas of Field 1 and Field 2. How does this sum compare to the area of Field 3?

7. The formula for area of a square can be written as [math]s^2[/math]. How does the area formula relate to the Pythagorean Theorem? How can we relate the area of the squares above to the Pythagorean Theorem?

10. Move the slider to "acute triangle." Compare the sum of the areas of Field 1 and Field 2. How does this sum compare to the area of Field 3?

9. In other words, if a triangle is a right triangle, then...

[math]a^2+b^2[/math]<[math]c^2[/math] [math]a^2+b^2=c^2[/math] [math]a^2+b^2>c^2[/math]

11. In other words, if a triangle is an acute triangle, then...

[math]a^2+b^2>c^2[/math] [math]a^2+b^2=c^2[/math] [math]a^2+b^2[/math]<[math]c^2[/math]

12. Move the slider to "obtuse triangle." Compare the sum of the areas of Field 1 and Field 2. How does this sum compare to the area of Field 3?

13. In other words, if a triangle is an obtuse triangle, then...