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Pythagores theorem

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Pythagores theorem

    • Posted by Mohit Thakur 5 years, 3 months ago

    CBSE > Class 10 > Mathematics
    • 3 answers

    Syed Sadiq Ahamed 5 years, 3 months ago

    The sum of hypotenuse is equal to the sum of other two side of triangle is called pythagoras theorem. AC²=AB²+BC²

    0Thank You

    Gaurav Seth 5 years, 3 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 BD AC

    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.

    ADB ABC

    So, (Sides are proportional)

    Or, AD.AC = AB2 ... (1)

    Also, BDC ABC

    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

    Confusion ??? Master ??? 5 years, 3 months ago

    Hypotenuse^2 = base ^ 2 + altitude ^ 2

    1Thank You

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