Question

show that a median of a triangle divides it into two triangles of equal area

Answer 1

Consider triangle ABC with the mid point D on the side BC and height AE

BD = DC ( D is the midpoint of side BC) ---------------------------------------1

Now consider triangle ABD 
Area of triangle ABD = 1/2 * base * height
                                  = 1/2 * BD * AE ------------------------------------------2

Consider triangle BDC
Area of triangle BDC = 1/2 *base * height
                                  = 1/2 * DC * AE ------------------------------------------3

From 1, 2 and 3 we come to know that,
 Area of triangle ABD = Area of triangle DBC

Therefore a median divides a triangle into two triangles of equal area.

Answer 2

in ΔABC, AD is the median
Hence BD = DC
Draw AE ⊥ BC
=1/2×AD×BD
Area of ΔABD
=1/2×DC ×AE
[since BD =DC]
= Area of ΔADC

Thus median of a triangle divides it into two triangles of equal area.

i hope it helps u .