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Question
Prove that the median of a triangle divides it into two triangles of equal area.
Solution
Draw AL perpendicular to BC.
Since AD is median of ΔABC. Therefore, D is the mid-point of BC.
⇒ BD = DC
⇒ BD x AL = DC x AL ...(multiplying by AL)
⇒ `(1)/(2)("BD" xx "AL")`
= `(1)/(2)("DC" xx "AL")`
⇒ ar(ΔABD) = ar(ΔADC).
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