Data : D and E are two points on BC such that BD = DE = EC.
To Prove: ar.(ABD) = ar.(ADE) = ar.(AEC)
Construction: Draw AM ⊥ BC.
[**Remark:** Note that by taking BD = DE = EC, the triangle ABC is divided into three triangles ABD,- ADE and AEC of equal areas. In the same way, by dividing BC into ‘n’ equal parts and joining the points of division so obtained to the opposite vertex of BC, you can divide AABC into ‘n’ triangles of equal areas.]