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E is any point on median …

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E is any point on median AD of a

    • Posted by Ravi Prem 4 years, 8 months ago

    CBSE > Class 09 > Other Subjects
    • 1 answers

    Sia ? 4 years, 8 months ago

    Given : E is any point on median AD of a {tex}\bigtriangleup{/tex}ABC
    To Prove : ar({tex}\bigtriangleup{/tex}ABC) = ar({tex}\bigtriangleup{/tex}ACE)
    In {tex}\bigtriangleup{/tex}ABC,
    As AD is a median
    {tex}\therefore{/tex}ar({tex}\bigtriangleup{/tex}ABD) = ar(ACD) [As a median of a triangle divides it into two triangle of equal areas] . . . (1)
    In  {tex}\bigtriangleup{/tex}EBC,
    As ED is a median,
    {tex}\therefore{/tex} ar({tex}\bigtriangleup{/tex}EBD) = ar({tex}\bigtriangleup{/tex}ECD) [As a median of a triangle divides it into two triangle of equal areas] . . . (2)
    ar({tex}\bigtriangleup{/tex}ABD) – ar({tex}\bigtriangleup{/tex}EBD) = ar({tex}\bigtriangleup{/tex}ACD) – ar({tex}\bigtriangleup{/tex}ECD)
    {tex}\Rightarrow{/tex} ar({tex}\bigtriangleup{/tex}ABE) = ar({tex}\bigtriangleup{/tex}ACE)

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