Question

A median of a triangle divides it into two triangles of equal areas.​

Answer 1

Answer:

Let ABC be a triangle and Let AD be one of its medians.

In △ABD and △ADC the vertex is common and these bases BD and DC are equal.

Draw AE⊥BC.

Now area(△ABD)=  

1/2 ×base×altitude of△ADB

=  1/2 ×BD×AE

=  1/2×DC×AE(∵BD=DC)

but DC and AE is the base and altitude of △ACD

=  1/2 × base DC × altitude of △ACD

=area△ACD

⇒area(△ABD)=area(△ACD)

Hence the median of a triangle divides it into two triangles of equal areas.