Question

prove that medians of triangle divide it two triangle of equal area

Answer 1

In ΔABC, AD is the median
Hence BD = DC
Draw AE ⊥ BC
Area of ΔABD 

= Area of ΔADC
Thus median of a triangle divides it into two triangles of equal area

Answer 2

let ABC be a triangle and let AD be one of its medians
to prove --ar(ABD)=ar(ACD)
const-draw AN perpendicular to BC

proof-of-concept ar(ABD)=1/2*base *height

ar(ABD)=1/2*BD*AN
ar(ABD)=1/2*CD*AN. (as BD=CD)
ar(ABD)=1/2*base *height (of triangle ACD)
ar(ABD)=ar(ACD)

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