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Prove that median of a triangle …

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Prove that median of a triangle divides it into two triangles of equal area

Posted by Gaurav Singh 8 years, 11 months ago

Neeraj Sharma 8 years, 11 months ago

$G i v e n : A ∆ A B C i n w h i c h A D i s m e d i a n$

$T o P r o v e : a r e a (∆ A B D) = a r e a (∆ A D C)$

$C o n s t r u c t i o n : d r a w A E ⊥ B C$

$P r o o f :$

$S i n c e A D i s M e d i a n o f ∆ A B C$

$\Rightarrow B D = D C$

$\Rightarrow B D \times A E = D C \times A E (M u l t i p l y i n g b o t h s i d e s b y A E)$

$\Rightarrow \frac{1}{2} (B D \times A E) = \frac{1}{2} (D C \times A E)$

$\Rightarrow A r e a (∆ A B D) = a r e a (∆ A D C)$

$H e n c e P r o v e d$

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