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    • Posted by Jatin Yadav 6 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 2 answers

    Gaurav Seth 6 years, 9 months ago

    Pythagoras Theorem

    Statement: In a right angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

    Given: A right triangle ABC right angled at B.

    To prove: AC2 = AB2 + BC2

    Construction: Draw BDAC

    Proof :

    We know that: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.

    ADBABC

    So,(Sides are proportional)

    Or, AD.AC = AB2 ... (1)

    Also,BDCABC

    So,

    Or, CD. AC = BC2 ... (2)

    Adding (1) and (2),

    AD. AC + CD. AC = AB2 + BC2

    AC (AD + CD) = AB2 + BC2

    AC.AC = AB2 + BC2

    AC2 = AB2 + BC2

    Hence Proved.

    1Thank You

    Mayank .?? 6 years, 9 months ago

    See textbook

    0Thank You

    ANSWER
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