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## An Introduction to the Pythagorean Theorem

Mathematicians have labored for ages to discover relationships within triangles along with other polygons. One of the famous and beneficial relationships ended up being uncovered by the Greek mathematician called Pythagorus. He found the sides of a right triangle are related in the following way:

When the lengths of each of the shorter two sides (the legs) of the right triangle are squared and the squares added together, the total is the same as the length of the 3rd side (called the hypotenuse) squared. So should you notice a right triangle, keep in mind that the lengths of the 2 smaller sides are related to the length of the longest side.

If an individual had time to form three external squares from each side of any right triangle, you will discover the smaller squares result in an interesting relationship as compared to the big square.

A triangle whose edges measure 3 units, 4 units, and then five units is one of the most well-known triangles in just about all of mathematics. Squaring each of the 2 smaller sides yields nine sixteen Equals 25 sq units. The longer side is five units, which means its square has an area of twenty-five square units. This arrangement holds true for each and every right triangle.

Many problems that deal with right triangles yield decimal answers. However, there are many examples of whole numbers combinations that are possible in right triangles. Some of these are:

three, four, five

six, eight, ten

five, twelve, thirteen

seven, twenty-four, twenty-five

eight, fifteen, seventeen

Each of the above combinations represent the three lengths of a right triangle. In class, teachers often begin to teach the concept of the Pythagorean Theorem using whole number examples. Later in class, many of the answers may contain one or more sides whose lengths are not whole numbers.

In a right triangle, the 2 smaller sides are legs and the longest side is known as a hypotenuse. Usually a stands out as the shorter of the two legs and b is usually the longer of the legs. In some cases, a is the identical length as b. All right triangles contain a lengthiest side that is directly across from the right angle. This longest side is represented by the variable “c” and it is referred to as the hypotenuse.

Frequently, major findings in science and math obtain distinctive names. Since this special relationship within right triangles was unearthed by Pythagorus, it has been referred to as Pythagorean Theorem in his honor.

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