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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 5 years, 3 months ago

CBSE > Class 09 > Other Subjects

1 answers

Sia ? 5 years, 3 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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CBSE > Class 09 > Other Subjects