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Show that in a right triangle …

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Show that in a right triangle the square of the hypotenuse is equal to this sum the square of the other two sides. Thus if ABC is an isosceles triangle right angled at c prove that a b square is equal to 2 AC square

    • Posted by Sahil Ansari 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 4 months ago

    Given : {tex}\triangle \mathrm{ABC}{/tex} is right angle at B
    To prove:  {tex}A C^{2}=A B^{2}+B C^{2}{/tex}

    Construction: Draw {tex}B D \perp A C{/tex}

    Proof:In {tex}\triangle{/tex}ABC and {tex}\triangle{/tex}ABD

    {tex}\angle{/tex}ABC={tex}\angle{/tex}ADB=90

    {tex}\angle{/tex}A is common 

    {tex}\angle{/tex}ABC{tex}\sim{/tex}{tex}\angle{/tex}ADB
    {tex}\Rightarrow \frac{A D}{A B}=\frac{A B}{A C}{/tex}
    {tex}\Rightarrow{/tex} AD. AC = AB2 ...(i)
    Similarly {tex}\Delta \mathrm{BDC} \sim \Delta \mathrm{ABC}{/tex}
    {tex}\Rightarrow \frac{C D}{B C}=\frac{B C}{A C}{/tex}
    {tex}\Rightarrow{/tex} CD.AC = BC2 ...(ii)
    Adding (i) and (ii) 
    AD.AC + CD. AC= AB2 + BC2
    AC(AD + CD) = AB2 + BC2
    AC {tex}\times{/tex} AC = AB2 + BC2
    AC2 = AB2 + BC2
    Hence Proved

    0Thank You

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