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An Introduction to the Pythagorean Theorem

Mathematicians have worked for ages to discover relationships between triangles and other polygons. One of those famous and useful relations was discovered by the Greek mathematician Pythagorus. He found that the sides of a right triangle are related in the following way:

When the lengths of the two shorter sides (legs) of a right triangle are squared and the squares are added together, the sum becomes a square equal to the length of the third side (called the hypotenuse). So you should find a right triangle, remember that the length of the 2 shorter sides is equal to the length of the longest side.

If someone had time to make three outer squares from each side of a right triangle, you would see that the smaller squares result in an interesting relationship compared to the larger square.

A triangle whose sides measure 3 units, 4 units, and then five units is almost certainly one of the most familiar triangles in mathematics. Dividing the square from each of the 2 smaller sides equals nine sixteen equal to 25 square units. The longest side is five units, so its square is twenty-five square units. This arrangement is true for any right triangle.

Many problems dealing with right triangles give decimal answers. However, there are many examples of combinations of whole numbers 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 represents three lengths of a right triangle. In the classroom, teachers usually begin teaching the concept of the Pythagorean Theorem using whole number examples. Later in the class, many answers may have one or more sides whose lengths are not whole numbers.

In a right triangle, the 2 shorter sides are the legs and the longest side is known as the hypotenuse. Usually a ends up being the shorter of the two legs and b is usually the longer leg. In some cases, a is the same length as b. All right triangles have a longest side that is directly above the right angle. This longest side is represented by the variable “c” and is called the hypotenuse.

In general, major discoveries in science and mathematics have different names. Since this particular relationship between right triangles was discovered by Pythagorus, it is named in his honor as the Pythagorean Theorem.

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