Pythagoras Trick

The Pythagorean Trick

What is the Pythagorean Trick?

The Pythagorean theorem is a fundamental theorem in mathematics that relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The Pythagorean trick is a simple method for finding the length of the hypotenuse of a right triangle without using the Pythagorean theorem. It is based on the fact that the square of a number is equal to the area of a square with that number as its side length.

How to Use the Pythagorean Trick

To use the Pythagorean trick, follow these steps:

1. Draw a square with the length of one of the legs of the right triangle as its side length.
2. From the opposite corner of the square, draw a diagonal line to the opposite side of the square.
3. The length of the diagonal line is equal to the length of the hypotenuse of the right triangle.

An Example of the Pythagorean Trick

Let's say we have a right triangle with legs of length 3 and 4. To find the length of the hypotenuse, we can use the Pythagorean trick:

1. Draw a square with side length 3.
2. From the opposite corner of the square, draw a diagonal line to the opposite side of the square.
3. The length of the diagonal line is equal to the length of the hypotenuse of the right triangle. In this case, the length of the diagonal line is 5.

Conclusion

The Pythagorean trick is a simple and effective method for finding the length of the hypotenuse of a right triangle. It is a useful tool for anyone who works with right triangles, such as carpenters, architects, and engineers.

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