Show that a median of a triangle divides it into two triangles of equal areas
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Let ABC be a triangle and Let AD be one of its medians. In $$\triangle ABD$$ and $$\triangle ADC$$ the vertex is common and these bases BD and DC are equal. Hence the median of a triangle divides it into two triangles of equal areas.
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Step-by-step explanation:
to prove:
ar(triangle ADB) = ar(triangle ADC)
=> 1/2 *b*h = i/2*b*h
=>1/2*BD*AD=1/2*AD*DC ....eqn 1
=> since BD=DC[AD is a median]
therefore, eqn 1 is true
hence, proved
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