Question

prove that median of tiangle divides it into two equal triangle

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

draw triangle ABC ,
AD is the median
BD = DC-------(1)
draw AM ⊥ BC
arΔABD/arΔACD = (1/2*BD*AM)/(1/2*DC*AM)


= (1/2*BD*AM)/(1/2*BD*AM) [ from (1)]
= 1

∴ arΔABD /arΔACD =1

arΔABD = arΔACD