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# Introduction

In the ancient world, buildings and monuments were often constructed using right-angled triangles.

The important rule about right-angled triangles was formulated by the Greeks, called the Theorem of Pythagoras.

In right-angled triangles, the side opposite to the right angle is called the **hypotenuse**, as illustrated below:

Remember sometimes that the triangle may be tilted, so it’s not always the same place. However, it is always opposite, relative to the 90 degree angle.

The **Theorem of Pythagoras** is that the square of the hypotenuse, is equal to the sum of the squares on the other 2 sides, i.e.:

The mathematical notation of the Pythagorean theorem for the above triangle is

For example:

Another example:

The opposite to square () is root (). So the (use a calculator to find out the root).

Another example:

Another example:

Word questions in Pythagorean, as in other areas of mathematics, are harder.