Show that a median of a triangle divides it into two triangle of equal area - Maths - Areas of Parallelograms and Triangles

Question

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

Ankush Jain · Accepted Answer

Consider a triangle PQR

Let PS be one of its medians

Now, PS is a median of âˆ†PQR drawn to the side
QR,

âˆ´QS = SR â€¦ (3)

Hence, from (1), (2) and (3), ar (âˆ†PQS) = ar
(âˆ†PSR)

Show that a median of a triangle divides it into two triangle of equal area.