Objective: Students will use Geometer's Sketch Pad to apply the Pythagorean Theorem and discover irrational numbers.
Description: This activity is suitable for various levels of middle school and high school students. Students whould know how to apply the Pythagorean Theorem but it is not necessary that they know what an irrational number is. This activity is a nice introduction to irrational numbers.
Activity:
*Let the congruent sides, a1 and a2, of the smallest right triangle piece of the GSP illustration be one (1) unit. (the grey piece). Use the Pythagorean Theorem to find the third side. Note that the angle between sides a1 and a2 is 90 degrees or a right triangle. Click here for the answer
*Discuss the value of the third side and why the value may have "bothered" Pythagoras. Click here for a discussion.
* Use the Pythagorean Theorem as well as manipulations of the GSP sketch to find the perimeter and area of each of the pieces of the sketch. Click here for the answers.
















* Try to form a square, not changing the shape of any pieces, using the following pieces of the sketch. You can print the GSP sketch and make tangrams for this excercise. These are all possible to contruct.
1. The two small triangles and the one medium triangle.
2. The two small triangles, the one medium triangle, the parallelogram, and the square.
* Why is it not possible to construct squares using the following pieces? You can print the GSP sketch and make tangrams for this excercise. Click here for an explanation.
3. All of the pieces except one of the large triangles.
4. Any six pieces.