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Congruent Triangles

Prove that a ...

Question

Prove that a median divides a triangle into equal parts

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Solution

$I n △ A B C, A D$ is median
$B D = D C$
$d r a w A E ⊥ B C$
area of $△ A B D = \frac{1}{2} \times B D \times A E [s i n c e B D = D C]$
=area of $△ A D C$
$∴$ Median of a $△ g l e$ divides it into two $△ g l e s$ of equal area.

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