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In triangle ABC, AD is perpendicular …

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In triangle ABC, AD is perpendicular to BC such that ADsq.= BD×CD. Prove that triangle ABC is right angled at A

    • Posted by Amritpal Deol 6 years, 5 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 5 months ago


    AD2 = BD {tex}\times{/tex} CD
    or, {tex}\frac { A D } { C D } = \frac { B D } { A D }{/tex}
    Therefore, {tex}\triangle A D C \sim \triangle B D A{/tex} (by SAS)
    or, {tex}\angle{/tex}BAD = {tex}\angle{/tex}ACD;
    {tex}\angle{/tex}DAC = {tex}\angle{/tex}DBA (Corresponding angles of similar triangles)
    {tex}\angle{/tex}BAD + {tex}\angle{/tex}ACD + {tex}\angle{/tex}DAC + {tex}\angle{/tex}DBA = 180o [sum of angles of ∆]
    or, 2{tex}\angle{/tex}BAD + 2{tex}\angle{/tex}DAC = 180o
    or, {tex}\angle{/tex}BAD + {tex}\angle{/tex}DAC = 90o
    Therefore, {tex}\angle{/tex}A = 90o

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