Pythagorean Theorem

Use the sliders to change the length of the legs of the right triangle. Notice how changes in the leg lengths affect the length of the hypotenuse. How are the areas of the corresponding squares related?

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Complete the following.

1. Use the sliders to discover 7 Pythagorean triples (pairs of legs that yield a whole number hypotenuse). For example, leg lengths of 3 and 4 yield a hypotenuse length of 5. One Pythagorean triple is 3-4-5. Find 6 others.

2. What happens to the length of "c" as the length of "a" approaches zero?

3. Is the area of square a <, >, or = to a²?
Is the area of square b <, >, or = to b²?
Is the area of square c <, >, or = to c²?

4. In general, how are the areas of the squares related to each other?

Wynn Essler, Created with GeoGebra