# Pythagorean Theorem Worksheet: Free Word, PDF

This year, many students will be learning about the Pythagorean Theorem in school. The simplicity of the Pythagorean Theorem worksheet is the best thing about it. It enables you to learn some of its basic properties while practicing graphing skills simultaneously. Over the years, many engineers and architects have used the Pythagorean Theorem worksheet to complete their projects.

## Who is Pythagoras? Biography

Born on the Greek island of Samos in the late 6th century BC, Pythagoras is considered one of the greatest mathematicians of antiquity. However, since no documents belonging to this period have survived to the present day, it cannot be clearly confirmed what he did on what date.

Although some biographies describing the life of Pythagoras have been found, they were all written long after Pythagoras died. Legend has it that a few months before Pythagoras was born, an oracle told his father that a very gifted being would come. Pythagoras’ name means ‘Pythian preached.’

As you can see, the reason is the predictions of the oracle. According to some records, when Pythagoras was just 18 years old, he not only participated in the Olympic war games but also won all the competitions. Pythagoras was an athletic and intellectual youth interested in Greek philosophy, history, and science. According to some historians, he was a student of another famous mathematician, Thales.

The Greek philosopher and mathematician, who went on different journeys to continue his studies, eventually went to Egypt. He tried to understand and learn the teachings of the Egyptian priests until 525 BC when the Persians invaded the country and took him prisoner in Babylon. While he was captured there, he spent all his time studying Babylonian knowledge. When he was allowed to return to the island of Samos, he began teaching in an amphitheater, but without much success.

In fact, he attempted to spread the knowledge that caused him to be expelled from this city as well. He decided to flee to Greater Greece to establish a school, teach and pursue his goal of continuing the tradition of the Greek philosophers.

Pythagoras made it a priority to apply mathematics to his philosophical thoughts throughout his life. Some of his students followed in his footsteps, embracing the same passion in their experience and research. They were so adopted that some began to suspect that Pythagoras’ school was a sect. Pythagoras died around 500 BC, but how he died is still unknown. Of course, there are no statements about it.

## Pythagoras Theorem (Formula and Proof)

Pythagoras’ most famous discovery is undoubtedly this theorem on right triangles. This theorem at first; is defined as “the sum of the areas of the squares on the right sides of a right triangle is equal to the area of the square on the hypotenuse.” The known expression of this theorem, which is still accepted today, is a²+b²=c².

When a square is formed from each side of the triangle, the areas of the squares are ordered a2, b2, and c2 based on the square area formula. Euclidean relation is established in the triangle with the perpendicular descent from the corner of the right triangle formed by the combination of the corners of all three squares to the parallel side of the square where the hypotenuse is located. The simplest way of proving the theorem, which has countless proofs, is the “rearrangement” method of Pythagoras, which is stated to belong to the philosopher and mathematician Proclus in some sources.

## The first known proof (Euclid’s proof) is based on:

c2 = a2 + b2 The length c is the hypotenuse. The lengths a and b are perpendicular sides. A square is created from each side. The areas of these squares are ordered as a2,b2, and c2 based on the square area formula. Thus, a right triangle is formed by joining the vertices of three squares. Euclidean relation is established within the triangle with the perpendicular descended to the side parallel to the hypotenuse of the square formed by the hypotenuse from the right corner of the triangle formed. (The Euclidean relation can be proved by similarity.)

### According to Euclid;

a2 = p(p+q)

That is, the square of one of the perpendicular sides is equal to the product of the length of the side adjacent to it from the parts separated by the perpendicular to the hypotenuse and the entire hypotenuse. In this situation

a2 = p.c.

Will be. That is, the area of ​​the square belonging to the side a will be equal to the area adjacent to it from the areas that the area of ​​the hypotenuse divides into two by the perpendicular descent. We consider this for the other side as well.

a2 = p.(p + q) b2 = q.(p + q)

p + q = c

a2 = p.c, b2 = q.c. Followed by,

a2 + b2 = p.c + q.c

a2 + b2 = c.(p + q)

p + q = c

a2 + b2 = c.c

a2 + b2 = c2

## Using Pythagorean Theorem worksheet

The Pythagoras Theorem worksheet is designed to help you review the knowledge related to geometry. By using the worksheet, you will be able to define each type of triangle and understand how to calculate its sides. More importantly, by using this worksheet, you’ll be able to apply the Pythagoras Theorem by completing problems.

With this Pythagoras Theorem worksheet, students are presented with a variety of triangles and must find the longest side. Students will be asked to identify whether the triangle is right-angled or not, whether it has an obtuse angle, and whether it is scalene or isosceles.

Each triangle is given as a diagram as well as a written description to help students understand what they should be looking for in each problem. These questions are ideal for helping students learn how to apply the Pythagorean theorem knowledge they have acquired so far in their studies while also providing them with new challenges so they can continue to enjoy this practice further!

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