## Pythagoras Theorem

A mathematical theorem that is used to state the relationship between the three sides of a triangle can be defined as the Pythagoras theorem**.** It is also referred to as the Pythagorean theorem. Before knowing about the details of the Pythagoras theorem, you must be aware of the sides of a triangle. A triangle is one of the geometrical shapes which consists of three sides. They are the hypotenuse, base, and perpendicular. The base can be defined as one of the sides of the triangle which is the bottom line of the triangle. Likewise, the side which is opposite the right-angled triangle and is regarded as the longest side of the triangle is known as the hypotenuse.

A side that makes a right angle with the base as its opposite side is known as perpendicular. All three sides can be found in a right-angled triangle. Now, according to the Pythagoras or Pythagorean theorem, the sum of the squares of the other two sides of the triangle (base and perpendicular) is equivalent to the square of the longest side i.e. hypotenuse. Let us assume that ABC is a right-angled triangle, then using the Pythagorean theorem, BC. BC = AB. AB. + AC. A.C., where BC is the hypotenuse, AB is the base and AC is the perpendicular.

## History of Pythagoras / Pythagorean Theorem

To recall, a mathematical theorem that is used to state the relationship between the three sides of a triangle can be defined as the Pythagoras theorem. The theorem of Pythagoras was founded or originated by a Greek Mathematician who was known as the Pythagoras of Samos. Earlier, he was known for his works in the field of philosophy. He formed a group of mathematicians who lived in his place like monks. They finally invented the theorem and gave the name after their master, Pythagoras. However, it is also said that the theorem existed in the civilization 1000 years ago after the Pythagorean theorem was evolved. Various historians also say it came from the Babylon city of Mesopotamia. It was used in making the architecture of houses and big buildings. People who used the route of rivers and seas used the Pythagorean theorem to move and sail through different places.

## Right-Angled Triangle

A triangle is a two-dimensional shape that is made up of three angles, vertices, and sides respectively. It is one of the basic shapes of geometry and can be classified into various types based on the sides and angles. One of those types is the right-angled triangle. A right-angled triangle is a type of triangle where one of the sides is equivalent to 90 degrees. We all are aware of the fact that an angle with 90 degrees is known as a right angle, thus right angle in a triangle is defined as a right-angled triangle. The Pythagorean theorem is relevant for the right-angled triangle. Some of its properties are:

- In a right-angled triangle, the largest angle always measures about 90 degrees.
- The largest side of a right-angled triangle is known as the hypotenuse which is always placed opposite the perpendicular.
- The sides of a right-angled triangle obey the rule of the Pythagoras theorem.
- A right-angled triangle may not consist of any obtuse angle in it. An angle whose measures are less than 180 and more than 90 degrees is known as an obtuse angle.

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