Question

Show that the median of a triangle divides it into two equal triangles of same area

Answer 1

let in triangle

ABC AM be median
BM=MC(m is the mid point of BC)
angle AMB=angle AMC=90
AM=AM
therefore triangle ABM is congruent to Triangle ACM by RHS rule
therefore area of triangle ABM=area of triangle ACM
therefore median AM divide triangle ABC into two triangle of equal area