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Activity Discussion Math Math

  • Aashutosh

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    June 2, 2021 at 8:22 pm
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    Pythagoras theorem states that “The square of the hypotenuse side is equal to the sum of squares of the other two sides in a right-angle triangle“. The longest side of the right-angle triangle is called the hypotenuse. Because it is opposite to the angle of 90 degrees. The other two sides are perpendicular and base.

    Let us consider the right-angle triangle ABC with 90 degrees at B and draw a perpendicular BD meeting AC at D as shown in the photo.

    According to the question: â–³ADB ~ â–³ABC

    Therefore, AD/AB=AB/AC (corresponding sides of similar triangles)

    Or, AB^2 = AD × AC ……………………………..……..(1)

    Also, â–³BDC ~â–³ABC

    Therefore, CD/BC=BC/AC (corresponding sides of similar triangles)

    Or, BC^2= CD × AC ……………………………………..(2)

    Adding the equations (1) and (2) we get,

    AB^2 + BC^2 = AD × AC + CD × AC

    AB^2 + BC^2 = AC (AD + CD)

    Since, AD + CD = AC

    Therefore, AC^2 = AB^2 + BC^2

    Hence, the Pythagoras theorem is proved.

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