Explain Pythagoras Theorem in Detail


    The Pythagoras theorem is named and termed after a very renowned Greek mathematician called Pythagoras. Pythagoras Theorem is a significant and extensively used topic in mathematics, which states down and explains the relationship between the sides of a right-angled triangle. It is also commonly known as the Pythagorean Theorem. The formula and the rules of Pythagoras theorem are explained in this blog with the help of a few examples:

    Pythagoras theorem is commonly used to find the length of a particular side and angle of the given triangle. With the assistance of this theorem, one can derive the base, perpendicular, and hypotenuse formulas. Now let us explore the concepts and topics under the Pythagorean theorem in brief.

    What is Pythagoras Theorem?

    Pythagoras theorem explains that in any particular right-angled triangle, the square of that hypotenuse side is equal to the sum of squares of the other two sides of that same triangle. The sides of the triangle are termed perpendicular, the base, and the hypotenuse. Here, the hypotenuse is the longest side and is opposite to the 90-degree angle in the triangle. The sides of a right triangle which have exclusive positive integer units, when squared, are put in an equation, thus called a Pythagorean triple.

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    Pythagoras Theorem Formula

    The given standard formula for the Pythagoras theorem is stated here below:

    In a triangle, let us take one, which is the perpendicular side, where 2 is the base of the triangle, 3 is the hypotenuse side. Hence, according to the definition, the Pythagoras Theorem formula is presented as:

    Hypotenuse2 = Perpendicular2 + Base2

    Where can we practice Pythagoras Theorem?

    • To know if a particular triangle is a right-angled triangle or no.
    • In a right-angled triangle, we can determine the length of any side if the other two sides of the triangle are provided.
    • To find the incline or the slope of a square.
    • In oceanography, the Pythagoras formula is used to estimate the speed of sound waves in the oceans.
    • Pythagoras theorem is also used in meteorology and aerospace to ascertain the sound source and its range in space.
    • We can use the Pythagoras theorem to find electronic components such as tv screens, computer screens, solar boards, etc.
    • We can use the Pythagorean Theorem to find the inclination of a distinct landscape.
    • In navigation, Pythagoras is used to finding the most precise distance between two given points.
    • In architecture and construction, one can use the Pythagorean theorem to find the incline of a roof, sewerage system, light poles, electric poles, etc.

    Why Pythagoras Theorem

    The Pythagoras theorem can be used in multiple situations. It can be used to find the steepness or inclination of the slope of the hills or roofs. It can also be practiced to find the distance between an observer on a given height and to the point on the ground from the tower or a building above which the observer is inspecting the point. It is mainly used in the fields of construction, planning, and architecture.

    Proving the Pythagorean Theorem

    • Get a paper pen and scissors, then follow these particular steps accurately: 
    • Firstly draw a right-angled triangle on paper, leaving plenty of space after.
    • Then draw a square along the triangle’s hypotenuse, which is also the longest side of a triangle.
    • Draw the same sized square on the other side of the hypotenuse drawn on the same paper.
    • Then continue to draw lines along the square.
    • Next cut out the shapes drawn.
    • Lastly, arrange the shapes so that one can prove that the big square drawn has the same area as the two squares drawn on the other sides. Thus, establishing Pythagoras theorem.


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